algebra 1 unit 7: polynomials and factoring answer keyalgebra 1 unit 7: polynomials and factoring answer key

-x+x+25. Answer: Factor the polynomial. = (5x + 1)(5x + 1) 8a + 1. Explain how you can use the graph to factor the polynomial x2 + x 6. There are no text boxes; this is the PDF in Google Slides. 2k 9 = 0 or k + 2 = 0 P = 8x + 240 in. Edit your all things algebra answer key unit 7 online Type text, add images, blackout confidential details, add comments, highlights and more. h 2h = 0 or h + 2 = 0 = 240, Question 12. y = 0 or y = 8 or y = -1/2 x(x 4) 3(x 4) y = x + 15 x > 0 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9. Answer: Question 3. = 3x(x + 1) + 2(x + 1) (m 3)(m 7) = m 10m + 21, Question 6. s 6s + 2s 2s + s 9 (0.5G + 0.5y)2 0.25G2 + 0.5Gy + 0.25y2. 7.2 Polynomial Division. (x2 + 2x 1) + (2x2 2x + 1) t = 0 or t = -2 We have to write the polynomial in standard form 3t(t + 2) = 0 x2 + 3x 4 MODELING WITH MATHEMATICS (x + 9)(x 9) (2x + 7)(2x 7) = 0 x(x + 2) 1(x + 2) = 0 d = B = 4, e. (x + 1)(x 3) = 0 Compare factoring 6x2 x 2 with factoring x2 x 2. Finding Binomial Factors x = 0 or x + 3 = 0 or x 3 = 0 VOCABULARY For each of the following, decide whether the property is true for 0, 1, both, or neither. 49a 14a + 1 Identify any x- and y-intercepts. 3x2 14x + 8 x = -6, 5 Given expression Also, check out the more Big Ideas Math Algebra 1 Answers to gain more marks in the examinations. = m(m 2m 8) A = x 12x How can you rearrange these regions to show that a2 b2 = (a + b)(a b)? x2 36 Find the perimeter of the projection when the height of the wall is 8 feet. The Punnett square shows the possible gene combinations of an offspring and the resulting colors. a. factoring by grouping, p. 404 Your membership is a Single User License, which means it gives one person you the right to access the membership content (Answer Keys, editable lesson files, pdfs, etc.) The degree is 6. x + 2x + 2 15 hours ago. Answer: (x 5)(2x 1) = 2x x 10x + 5 = -8x + 9x 12 + 4 a. = 2209 1936 ac = pq ABOUT THIS RESOURCEThis Polynomials & Factoring is a complete curriculum unit bundle that contains guided notes, practice worksheets, homework assignments, a mid-chapter quiz, a factoring quiz, a study guide, and an end of unit test that covers the following topics:Classifying Polynomials by Deg. = p 5p 24 = z 11z + 11z 121 x + x 2 = 0 b + 5 8b + 10 = 0 v + 13v 2v 26 = 0 x(4x + 25x 56) = 0 Find the width. Find the width of the entrance at ground level. Answer: 6x 7x + 9 1 Question 2. 4(4x 9) = 0 Examples of Polynomials. What is the area of the square plot of land? 6x2 + 17x + 7 Question 31. Answer: Algebra 1. = 4x 16, Question 15. = (h + 2)(-8h + 3), Question 22. o. x + 2x + x = x(x + 2x + 1) = x(x + 1) C. Question 3. The x-intercept does not exist as it is an increasing function. Question 1. HOW DO YOU SEE IT? Are both solutions of the equation reasonable in the context of the problem? THOUGHT PROVOKING w - 4 answer choices Is not a difference of squares Is a difference of squares; (w - 2) (x + 8)(x 9) = 0 Answer: (v 3)(v2 + 8v) = v(v2) + v(8v) 3(v2) 3(8v) (5p + 2) = (5p) + (2) + 2(5p)(2) Sorry, the content you are trying to access requires verification that you are a mathematics teacher. a. Write a polynomial that represents the total amount spent each year on buying new and used vehicles in the 7-year period. It is in the form of (a + b)(a b) = a b -3x2 x + 2 s(s 20) + 3(s 20) = 0 Question 2. Answer: 96 = (x + 8)(x)(x 2) y = -4|x + 2| Unit 7 - Polynomials These lessons introduce polynomials as analogous to the integers and multiple parallel are drawn to the integers throughout the unit. (x + 4)(x2 + 3x + 2) x 3x 4x + 8x + 3 2 Then classify the polynomial by the number of terms. Group the first two terms together and then the last terms together. 4x-5 = 4 or 3x = 9 (-5k + 3)(k + 5), Solve the equation. r 6r + 9 _____ Unit 7: Polynomials & Factoring Date: . y = -2, 6. (20 + 1) = (20) + (1) + 2(20)(1) 2y 12y + 18y h3 + 2h2 9h 18 Question 9. = (2x + 1)(2x 1), b. t2 t2 10t 8k2 + 80k + 200 q = -3/4, -2, Question 12. 4x(x 5) + 1(x 5) A contractor extends a house on two sides. 2x + 12x 4x 4x 24x + 8 3x 12x 1x + 4 = 0 MODELING WITH MATHEMATICS 29 = (30 1) 25x2 10x + 1 THOUGHT PROVOKING Answer: Question 2. (6x 3y)2 = 3[9m 6m 6m + 4] -5k 25k + 3k + 15 \(\frac{4}{3}\)x + \(\frac{4}{9}\) = -x2 n = 2 or n = -18/2 or n = 2 What are the patterns in the special products (a + b)(a b), (a + b)2, and (a b)2? PROBLEM SOLVING c = mn There are three terms in the given polynomial. h3 + 4h2 25h 100 Write the prime factorization of the number. (7m + 8n)(7m 8n) = (7m) (8n) x x 2 + 7x x x2 + x 30 We have to write the polynomial in standard form Answer: In Exercises 310, find the product. Write an equation of the form x2 + bx + c = 0 that has the solutions x = -4 and x = 6. n 5n = 24 (w + 9)(w + 6) = w(w) + w(9) + w(6) + 9(6) Question 4. x x 2 = 0 a = 3/2, -1/5, 7.7 Factoring Special Products (pp. (b + 13)2 = 0 Write a polynomial that represents the area of the blanket including the fringe. 6m(m + 2) = 0 282 242 Explain. Answer: Question 4. So, the equation will have real roots stating that the stage satisfies his requirements. We value your feedback about our products and services. Answer: Answer: Question 52. Factor out a GCF from each separate binomial. A = (36 + x 12x) Answer: Question 44. h = x 2 Describe a strategy for recognizing which polynomials can be factored as special products. Question 25. 2x = y + 2 = (m + 12), Question 22. HOW DO YOU SEE IT? x = -7/3, -1/2, Question 28. 28, 64 Area = length width -w(w 16) -36(w 16) = 0 d. (2x 3x) (x2 2x + 4) Answer: -3x 3x + 2x + 2 Your friend is not correct. 2x + 3x 2 + 6 10 m = (10 + m)(10 m), Question 3. Write the product represented by the algebra tiles. Let M=23-1=7. (use paper and pencil methods and . = (s 5)(s 10) Answer: Question 36. (n 3)(n 6) = 0 m3 2m2 8m Please do not copy or share the Answer Keys or other membership content. The Parthenon in Athens, Greece, is an ancient structure that has a rectangular base. It is in the form of (a + b)(a b) = a b t(t2 5t + 1) 2(t2 5t + 1) = m(m 1) 1(m 1) m2 49 x = 2 = x 2 = 0 (3p + 7)(3p 7)( p + 8) = 0 9a2 - 121 6. (x + 2)(2x 1) = 2x + 3x 2 Answer: Answer: Question 2. The x-axis represents the ground. What percent of the possible gene combinations result in albino coloring? Given, = 16c + 16d + 32cd Question 17. = (v + 1)(-7v 12), Question 20. c = 3, 4, Question 9. Answer: If there are only two terms then look for the sum of cubes or differences of squares or cubes. Answer: Solve the equation. a. x 3x + 2 Question 6. e. x 2x 3x = x(x 2x 3) = x(x 3x + 1x 3) = x(x(x 3) + 1(x 3)) = x(x 3)(x + 1) N b + 13 = 0 The amount of money you have after investing $400 for 8 years and $600 for 6 years at the same interest rate is represented by 400x8 + 600x6, where x is the growth factor. So, the width is x + 11. b. (\(\frac{1}{2}\) c )(\(\frac{1}{2}\) + c ) So, the factor pairs of 18 are 1, 2, 3, 6, 9, 18. Answer: w = 16 or w = -6 Answer: Answer: y2 2y 8 = 7 Work with a partner. z(z + 9) 2(z + 9) Because it is not in the form of (a + b)(a b). The box has a length of x feet, a width of (x 1) feet, and a height of (x + 9) feet. = d(2d2 d + 7) + 6(2d2 d + 7) Question 4. 25x2 10x + 1 \(\frac{4}{9}\) (-r 10) (-4r3 + r2 + 7r) \(\frac{5}{3}\)y Answer: 3.7k plays . MODELING WITH MATHEMATICS Sign, fax and printable from PC, iPad, tablet or mobile with pdfFiller Instantly. -x 8 = -y x + 8 = y REASONING b. x3 6x2 + 9x = 18m + 194 Explain. b = -10, -8, Question 23. 48 = 24 16y2 - 25 4. y2 + 49 5. The coefficient of the polynomial is 3, 7.4, -1.3 a + c = 1 (2y + 4)(2y 4) Wondering how to ace up your preparation for Chapter 7 Polynomial Equations and Factoring? (c2 6d2) + (c2 2cd + 2d2) OPEN-ENDED -3x(x + 1) + 2(x + 1) n(n 9) Find the degree of the monomial. Answer: Question 22. (-5g 2h)(-5g + 2h) Given equation (n 1)(n + 6)(n + 5) = 0 Question 9. 3t2 + 16t 12 Answer: (x + 8)(4x 7) = 0 (f + 1) Question 4. ERROR ANALYSIS In Exercises 31 and 32, describe and correct the error in finding the product. n2 12n + 35 The polynomial expression that represents the area of the potato . = 841, Question 30. Algebra 1 unit 7 test polynomials and factoring answer key Play this game to review Algebra I. Explain your reasoning. Find the width of the tunnel at ground level. Describe two ways to determine the percent of possible gene combinations that result in green pods. y = 4x + 25x 56x Answer: Question 54. If you need to purchase a membership we offer yearly memberships for tutors and teachers and special bulk discounts for schools. = 2x + 1, Question 3. (t + 2)(-2t + 5) = 0 The coefficient is 9. Answer: 1 = 2d or 1 = -2d The polynomial -16t2 25t + 200 represents the height of the penny after t seconds. Answer: Question 10. y + 2 = 0 or y 6 = 0 Unit 7: Polynomials Answer Keys PL1: I can name a polynomial by number of terms and degree. Question 1. a2 + 5a = 0 16t2 v0t s0 x = 1 = x 1 = 0 Factoring x2 + bx + c When c Is Positive, p. 386 x(x 1)(x + 9) = 72 a. = t 7t + 11t 2. (-k + 5) (3k2 6) = -3k k + 11. Area after entering/Area before entering = (2 12(2) + 36)/(4 12(4) + 36) Your friend says that when adding polynomials, the order in which you add does not matter. Question 41. but is not meant to be shared. = 9[(r 5)(r + 1)]. The second binomial is -8x 9, b. y + 15y 2y 30 Combined length is equal to the sum of lengths of the photo and the frame. Question 1. = a + 3a + (a + 3) The golf ball does not hit the pine tree. (x + 1)(x + 1)(-2) = (x + 1) 2 = x + 2x + 1 2 = x + 2x 1 Factors of 75 are 1, 3, 5, 15, 25 and 75 Question 8. c. c2 + 2 + c z = -3 or z = 7 x2 13x + 22 = (x 11)(x 2), Question 12. c 3c 4c + 12 = 0 Question 47. Is your friend correct? Answer: = (106)(2) Explain. (w + 6)(w + 7) (x + 4)(x + 3). The degree of c is 3 Question 9. x = -1, -8, Factor the polynomial. 4z + 6z 2z 3 All Things Algebra Unit 7 Answer Key Make these fast steps to change the PDF Unit 7 polynomials and factoring homework 1 answer key pdf online free of charge: Register and log in to your account. x2 9 a = 0, -5, Question 9. x(x 1) = 0 The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. (4y 7)(y 4) = 0 So, (x + 1)(x2 + 5x + 8) = x + 6x + 13x + 8, Question 10. V = x + 16x. x 2x + 3x 6 2z(2z + 3) 1(2z + 3) y = 4x + 11x 3 d = 2, -6, -8, Question 7. y 7y 30 = 0 = 3y 7y 40, Question 11. = 3s 3 + 5 i. x x = x(x 1) I (t 7)(t + 7) z(z 7) + 3(z 7) 1. x 2x 3 = 0 18q 2q2 = 0 e. (x 2)2 How many x-intercepts does the graph of y = (2x + 5)(x 9)2 have? 2 : 5 . Factoring Difference of Squares Directions: Factor each polynomial, if possible. y = 16t + 8t The cost (in dollars) of making b necklaces is represented by 8b + 6. = \(\frac{1}{4}\) c, Question 22. -3x2 x + 2 PROBLEM SOLVING v2 + 11v 26 = 0 = n 5n + 10n 12 2k = 9 or k = -2 ERROR ANALYSIS In Exercises 23 and 24, describe and correct the error in factoring the polynomial. 23x4 Question 4. x 1x 2x + 2 (5s + 6)(s 2) A = x(x 12) Question 1. If you are not 100% satisfied, we will refund you the purchase price you paid within 30 days. -p2 + 4p p2 + 3p 15 x + 8x 9x 72 = 0 Answer: (y + 9)(y2 + 2y 3) Sitemap. Write the polynomial in standard form that represents the area of the patio. The Gateway Arch in St. Louis can be modeled by y = \(\frac{2}{315}\)(x + 315)(x 315), where x and y are measured in feet. = y + 4y + 6y + 24 Explain. = -8x 12 + 9x + 4 (x 4)(x 7) Answer: (z 2)(z + 6) (6x 3y) = (6x) + (3y) 2(6x)(3y) These worksheets focus on the topics typically covered in Algebra I Multiplying Monomials Worksheet Multiplying and Dividing Monomials Sheet Adding and Subtracting Polynomials worksheet Multiplying Monomials with Polynomials Worksheet Multiplying Binomials Worksheet Multiplying Polynomials Simplifying Polynomials Like Terms Factoring Trinomials Answer: Question 30. MODELING WITH MATHEMATICS Answer: Question 10. What does it mean for a polynomial to be factored completely? Write a polynomial that represents the area of the picture frames, not including the pictures. c. The guitar costs $1100. Sign it in a few clicks Draw your signature, type it, upload its image, or use your mobile device as a signature pad. Write a polynomial equation in factored form that has three positive roots. MODELING WITH MATHEMATICS Answer: Question 46. z = -3 or z = 25 Question 43. x2 + 5x = 0 5(2r + 1) 3(-4r + 2) a. Answer: It is in the form of (a b) = a + b 2ab Question 5. p 9 = 0 COMPARING METHODS 3x 6x + 9 7x 1 Find the sum or difference. (z 2)(z + 6) How does this value relate to the graph? 4y2 - 81 8. RIGOROUS. The width of a box in the shape of a rectangular prism is 4 inches more than the height h. The length is the difference of 9 inches and the height. Explain how you can determine whether a polynomial is a perfect square trinomial. 2x + x 10 = 0 w2 \(\frac{7}{3}\)w + \(\frac{49}{36}\) = 0 Answer: a. x3 25x = 0 Draw the rectangular array of algebra tiles that models each product of two binomials. Explain your reasoning. c. x3 + 6x2 + 9x= x(x + 6x + 9) = x(x + 3), Factor the polynomial by grouping. 2x + 7 = 0 or 2x 7 = 0 = x + 5x + 3x + 15 a. You can model the entrance to a mine shaft using the equation y = \(\frac{1}{2}\)(x + 4)(x 4), where x and y are measured in feet. = 4x + 12x + 8x 3x 9x 6 a. the set of negative integers; multiplication d. (-x 2)(x 3) Answer: Question 26. 02. Please dont change or delete any authorship, copyright mark, version, property or other metadata. MODELING WITH MATHEMATICS It is in the form of a b = a + 36 12a Answer: x = 0 or x = 3 (-1) + 6(-1) 4(-1) = 24 In Exercises 2938, solve the equation. = -3p + 5p 2p p 8p 15p (2y + 4)(2y 4) = (2x) (4) What do the signs of the terms tell you about the factors? 4x 9 = 0 A = 2x 14x An equation is considered to be in factored form when the product of the factors is equal to 0. x 5 = 0 or x 6 = 0 The area of the new parking lot is represented by (100 x)(100 + x). Answer: Question 41. 39 36 a. x3 + 4x2 + 3x = x(x + 4x + 3) = x(x + 3x + 1x + 3) = x(x(x + 3) + 1(x + 3)) = x(x + 1)(x + 3) Write a polynomial that represents the area of your pupil. t = 0 or t = 3/2 4x 4x 2x + 2 = x(x2 + 7x) + 4(x2 + 7x) = x + 3x 16x + 12. Describe and correct the error in solving the equation. 3x 2x 1 x(x 6) + 3(x 6) = 0 p 5 = 0 or p + 7 = 0 c positive Answer: Answer: Explain your reasoning. a(a + 3) + 3(a + 3) = 0 There are 3 terms in the polynomial so it is a trinomial. The degree of the monomial is 2+4=6, Question 12. What is the greatest common factor of the terms of 3y2 21y + 36? Given, Opposite signs on the constants will result in a negative value for c when multiplying the factors. a. A = 520 So, the t is 5/2. 542 522 Question 1. x 2x + x 12x = 2x 14x Question 3. 4d 6d + 3d 10d 7d + 2 Answer: Answer: y(y + 8) + 5(y + 8) x = 24 = 4.9 in. v = -13, 2, Question 34. 33 27 = (30 + 3)(30 3) So, (a 6)2 = a + 36 12a, Question 6. Answer: s2 + 20s + 100 = 0 10 Answer: Question 42. = 12y + 7y + 20y 7, Find the product. = h(h + 2) -2h(h + 2) y = -1(x + 4)(x 4) t = 6 or t = 2/3 Total area = x + 3x + 12x = 4x + 12x (-x2 + 9xy) (x2 + 6xy 8y2) Write the polynomial in a standard form that represents the balance of your account after 2 years. b. For each level, write a polynomial in standard form that represents the area of that level. PROBLEM SOLVING q(x) = 1/2 x 1/2. Area of square = s s Question 2. 5.2 Power Functions and Polynomial Functions. Factoring by Grouping, p. 404 h = x 2 -4 2 = -6 The area of the invitation is 15 square inches. g = 8, Question 17. (4m2 m + 2) (-3m2 + 10m + 4) The right side of the equation of each line is a polynomial. (x + 3)(x 2) = x + x 6, Use the Distributive Property to find the product. -3x4 24x 45x = 0 -16t + 8t 1 = 0 ABSTRACT REASONING Question 5. h 8 = 0 Add 6x5 10x2 +x 45 6 x 5 10 x 2 + x 45 to 13x29x +4 13 x 2 9 x + 4. -5s + 2s s 9 (-3n2 + n) (2n2 7) Number of terms = 1 20 is less than 30 therefore the side of square is 50m. So, the combined area is 624 sq. Answer: Question 41. -12y + 8y3 = 6w + 10w 9w 15, Question 6. Please click the link below to submit your verification request. 377382), Solve the equation. P = 68 ft, Polynomial Equations and Factoring Maintaining Mathematical Proficiency Page 355, Polynomial Equations and Factoring Mathematical Practices Page 356, Lesson 7.1 Adding and Subtracting Polynomials Page (357 to 364), Adding and Subtracting Polynomials 7.1 Exercises Page (362 to 364), Lesson 7.2 Multiplying Polynomials Page (365 to 370), Multiplying Polynomials 7.2 Exercises Page (369 to 370), Lesson 7.3 Special Products of Polynomials Page (371 to 376), Special Products of Polynomials 7.3 Exercises Page (375 to 376), Lesson 7.4 Solving Polynomial Equations in Factored Form Page (377 to 382), Solving Polynomial Equations in Factored Form 7.4 Exercises Page (381 to 382), Polynomial Equations and Factoring Study Skills: Preparing for a Test Page 383, Polynomial Equations and Factoring 7.17.4 Quiz Page 384, Lesson 7.5 Factoring x2 + bx + c Page (385 to 390), Factoring x2 + bx + c 7.5 Exercises Page (389 to 390), Lesson 7.6 Factoring ax2 + bx + c Page (391 to 396), Factoring ax2 + bx + c 7.6 Exercises Page (395 to 396), Lesson 7.7 Factoring Special Products Page (397 to 402), Factoring Special Products 7.7 Exercises Page (401 to 402), Lesson 7.8 Factoring Polynomials Completely Page (403 to 408), Factoring Polynomials Completely 7.8 Exercises Page (407 to 408), Polynomial Equations and Factoring Performance Task: The View Matters Page 409, Polynomial Equations and Factoring Chapter Review Page (410 to 412), Polynomial Equations and Factoring Chapter Test Page 413, Polynomial Equations and Factoring Cumulative Assessment Page (414 to 415), Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 1 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 1 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 2 Answer Key. 3z(z + 9) -1(z + 9) Click on the respective link and kickstart your learnings. 3. Unit 7 Polynomials and Factoring Worksheet Answers Unit 7 Polynomials And Factoring Gina Mount Wilson Answer Key. (-12 n) = (-12) + n 2(-12)n Answer: Question 4. Answer: Question 40. a. x(x) + x(-2) + 3(x) + 3(-2) Answer: Determine if the polynomial is a difference of squares and if it is factor the polynomial. \(\frac{x^{5} \cdot x}{x^{8}}\) Which expression does not belong with the other three? -3x(x 5) -1(x 5) = 0 V = 4x + 9x x 6. Answer: The number of individual memberships at a fitness center in m months is represented by 142 + 12m. y 12y + 36 = 0 by tfgiles4107. It is in the form of (a b)2 = a 2ab + b w 1w 3w + 3 = m 10m + 21 a. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at allthingsalgebra@gmail.com. x(x 9) = 0 1000 + 2000r + 1000r Explain what the roots mean in this situation. (6x + 9) (7x + 1) = -x + 8. 16: 1, 2, 4, 8, 16 = x + 4 + 4x, f. (3x + 1) Answer: Answer: Question 45. (-6) + 6(-6) 4(-6) = 24 (x 4)(x + 2) Let us find the area of level 1 of the deck. 2z4, 3y Answer: b. 4x + 11x 3 = 0 (w + 9)(w + 6) (r 5)(2r 1) b 10 + 4b 3 Question 1. x + x 6 Answer: Question 24. m = 0, -2, Question 34. 21 = (20 + 1) Tell whether the polynomial can be factored. To read the Single User License Agreement, please clickHERE. Answer: Answer: (p + 3)(p 8) = p(p 8) + 3(p 8) It is in the form of (a b) = a + b 2ab Big Ideas Math: Algebra 1 1st Edition ISBN: 9781608404520 Alternate ISBNs Boswell, Larson Textbook solutions Verified Chapter 1: Solving Linear Equations Page 1: Try It Yourself Section 1.1: Solving Simple Equations Section 1.2: Solving Multi-Step Equations Section 1.3: Solving Equations with Variables on Both Sides Section 1.4: All Things Algebra 1 CurriculumWhat does this curriculum contain? t(t + 9) 8(t + 9) = 0 e. (-x + 1)(x + 1)(-x) = (1 x)(-x) = -x + x y = 0, 8, -1/2. v 7 = 0 or v + 6 = 0 y > \(\frac{1}{2}\)x + 3 (p + 7) (6p2 + 13p) _____ F 34 Simplify. (6v2 + 2v 9)(4 5v) b. Answer: Determine the cost of the patio when x = 9. Given, Answer: A polynomial is a perfect square trinomial if the first and last terms are perfect squares, and the middle terms coefficient is twice the product of the square roots of the first and last terms. 3z2 + 26z 9 Is it possible to factor the trinomial 2x2 + 2x + 1? (4x + 3) + (x 2) Work with a partner. (x + 3)(x + 5) = 0 (4q + 3)(q + 2) = 0 Answer: The width of the frame is the same on every side, as shown. Question 45. 3p + 7 = 0 or 3p 7 = 0 or p + 8 = 0 Answer: n3 9n x3 + 2x2y x 2y A = 624 sq. The figure shows a large square with an area of a2 that contains a smaller square with an area of b2. Answer keys are for teacher use only and may not be distributed to students. = (5x) 1, Factor the polynomial. The Punnett square shows the possible gene combinations of the offspring of two Gy pea plants and the resulting pod colors. (6x + 9) (7x + 1) (n + 2)(n2 + 3) The cost (in dollars)of making b bracelets is represented by 4 + 5b. f. (x 6)(x 1) = 0 y 5y + 3y 15 = 0 h + 9h 3h 27 = 0 Answer: Core Vocabulary (x + 1)(x + 7) = 0 MODELING WITH MATHEMATICS Answer: Write the absolute value function as a piecewise function. Is your friend correct? The exponent is 4, Question 8. 7c3d2 x2 11x + 28 Combine the like terms to add or subtract the polynomials In Exercises 3542, find the product. Answer: The coefficient is \(\sqrt{7}\). 4x 49 = 0 Use algebra tiles to complete the rectangular array at the left in three different ways, so that each way represents a different special product. b 3 = 0 or b 5 = 0 2x(2x + 1) 1(2x + 1) 4y 7y + 28 = 16y Give another example of multiplying two binomials using algebra tiles that is similar to those in Exploration 2. (v 3)(v2 + 8v) What is the width of the patio? = 4. -3n + n 7 So, z = -3, 7, Question 19. x \(\frac{4}{3}\)x + \(\frac{4}{9}\) = 0 b. Answer: The sum of two polynomials is always a polynomial. The expression 1000(1 + r )2 represents the balance after 2 years, where r is the annual interest rate in decimal form. x(x + 3) + 5(x + 3) = 0 (x + 22)(x 15) = 0 x = 1 = x 1 = 0 Squaring on both sides [PDF] Gina Wilson Algebra Packet Answers 4. -2y2 5y 3 Write the product of two binomials modeled by each rectangular array of algebra tiles. Given, y = 7 The x-tiles on the board determine what the constants are in the factors. 20, 36 Answer: 2y(y 9)(y + 4) = 0 Explain. p + 2(15)(p) + 15 2 . ( p + 4)2 Send the new Algebra 1 Unit 7 Polynomials And Factoring Answer Key in a digital form when you finish completing it. Factors of 81 = 1, 3, 9, 27, 81 (t 2) U = -0.38t2 + 1.5t + 42 5p(2p 3)(p + 7) = 0 COMPARING METHODS The combined length is equal to the sum of lengths of the photo and the frame. \(\frac{4}{3}\)x + \(\frac{4}{9}\) = -x2 (2x 1)(2x + 1) Answer: In Exercises 2130, use the FOIL Method to find the product. Answer: Question 53. 8x 2x 2 The Punnett square shows the possible gene combinations of an offspring and the resulting colors. 2x3 2x Answer: Answer: Answer: Question 38. \(\sqrt{81}\) So, (p + 3)(p 8) = p 5p 24, Question 4. Question 27. x 72 = 0 or x + 72 = 0 (x 4)(3x 1) = 0 x = 0, -3, 3 = (3x) + (1) + 2(3x)(1) Answer: Essential Question How can you use algebra tiles to factor the trinomial x2 + bx + c into the product of two binomials? \(\frac{2}{3}\)m4 \(\frac{5}{6}\)m6 Question 50. f. 3b6 12b8 + 4b4 (y + 15)(y 2) Dogs are domesticated mammals that belong to the Canidae family. 3y = 21y = 7b(2b + 1) 2(2b + 1) = 0 0. w = 48 + 4 + 4 = 56 in. Answer: Question 56. The degree of a monomial is the sum of the exponents of the variables. Question 3. So, d = 1/2, -1/2, Question 16. Answer: Answer: Answer: (x + 1)(x + 8) m + 24m + 144 h = 12 in. Question 19. Answer: Describe a strategy for factoring the trinomial x 2 + bx + c that does not use algebra tiles. Answer: Answer: Question 26. 2w + w 136 = 0 9z + 18z + 18z + 36 Answer: (z + 3)(z 7) = 0 The coefficient of the polynomial is -8 The greatest common factor of 20 and 36 is 4. Question 8. Given, (2z 1)(2x + 3), Question 16. A = 10x + x 12x = x 2x p = 9 x = 1, 6. REPEATED REASONING 3x3 9x2 54x = 0 z2 4z 21 5z + 2z3 + 3z4 MODELING WITH MATHEMATICS x(x 2) + 3(x 2) Hint: Add the 2 sides together and subtract from the perimeter! -3q4rs6 The dimensions of the birdhouse in terms of its width are shown. Answer: Explain. examples 1. 03. = (m 1)(m 1), Question 10. So, (x + 7) = x + 49 + 14x, Question 2. 5p6 -3p3 4 The name of the polynomial is trinomial. = (x + 6)(x 3x + 2) Answer: b(b 3) -5(b 3) = 0 Question 61. 4(h + 6) (h 2) = 2x + 48 A = (6 + x 2.6(x)) Write a polynomial in standard form that represents the area covered by the hour hand in one rotation. = 4x + 1 4x z + 9z 2z 18 (x2 + 2x 1) + (2x2 2x + 1) Answer: 2y3 12y2 + 18y Answer: r = 0 or r = -7. y = 4x + 8. -22d + 29d 9 (6x + 9) (7x + 1) = (z + 9)(z 9), Question 6. Finding Binomial Factors Given, When multiplying two binomials, explain how the degree of the product is related to the degree of each binomial. Question 1. It is in the form of (a + b)2 = a + 2ab + b Given expression f(x) = a(x h)(x k)(x r) = 3[3v(2v 3) + 2(2v 3)] h3 + 2h2 9h 18 Answer: Question 26. Answer: l = 16 in Question 47. z2 + 10z + 21 = (z + 7)(z + 3), Question 6. z2 + 7z 18 = (z + 9)(z 2), Question 18. A = x 2(15)x + 15 (2x + 5)(x 2) 1.1 Exponents ; 1.2 Absolute Value; 1.3 Radicals; 1.4 Rationalizing ; 1.5 Functions ; 1.6 . The x-axis represents the ground. It is in the form of (a + b)(a b) = a b OPEN-ENDED 4r + 28r = 0 y = \(\frac{2}{315}\)(x + 315)(x 315) It is in the form of (a + b) = a + b + 2ab (n 3)(n2 2n + 4) MODELING WITH MATHEMATICS n = 2 or \(\frac{2}{3}\)n = -6 or n = 2 = 3x(2x 3) + 1(2x 3) Using these materials implies you agree to our terms and conditions and single user license agreement. Answer: v(v 7) + 6(v 7) Factor the polynomial. Share your feedback, including testimonials, on our website or other advertising and promotional materials, with the understanding that you will not be paid or own any part of the advertising or promotional materials (unless we otherwise agree in writing ahead of time). Factor a difference of squares. DIFFERENT WORDS, SAME QUESTION Unit 3) Functions. 2k + 4 + k 3 = 0 Answer: Then order the polynomials by degree from least to greatest. (t 2)(t2 5t + 1) Write a polynomial that represents the volume of the box. Find the greatest common factor. = x(x 3) + 2(x 3) = n(n2 2n + 4) 3(n2 2n + 4) (r3 6t4)(r3 + 6t4) 3s = 0 or s 3 = 0 -20.5 is same as -20.5x0 since anything to the zero power is equal to 1. = x 4 = v + 5v 24v. x2 + 27x + 176 = 20(2x + x 10) Answer: Question 56. Classify each polynomial by the number of terms. Answer: Answer: p + 30p + 225 (2x + 1)(2x 1) = 4x 1, Question 7. Question 35. Question 31. (2x + 1)(2x 1) = (2x) (1) d = -7, Question 14. w = 16 + 2x The volume of the composite solid is equal to 25x. We can write it as 15x 2x 8 c 7c + 12c = 0 Determine whether the set is closed under the given operation. MODELING WITH MATHEMATICS Answer: Answer: = z 121. The prime factorization of 96 are 2 2 2 2 2 3. Given the polynomial, which shows the terms Simplify the expression: (a + 2)(3a - 1). b. = 1/2 (x 7)[x + (x + 11)] (3a + 7) + (a 1) Step 3: Apply the zero-product property and set each variable factor equal to zero. Answer: MODELING WITH MATHEMATICS How wide is the reserve? (k3 7k + 2) (k2 12) Write a polynomial that represents the perimeter of the golf hole. Answer: (2k 4)(2k + 4) What is the area of the extension? It is a linear function. -12y + 8y3 Answer: w = 0 or w = 6 2 n = 0 or 6 + \(\frac{2}{3}\)n = 0 or n 2 = 0 w = 6 in The degree of the polynomial is 4. x \(\frac{2}{3}\) = 0 Question 1. 2x 4 and x2 + 6x 2 Answer: (-4) + 6(-4) 4(-4) = 24 Question 43. Question 35. h(x) = 21x2 37x + 12 we have c is positive, the constant terms in each factor must have the same signs. s 5 = 0 or s 10 = 0 0.5B + 0.5W b + d = 0 How many times greater is the area of your pupil after entering the room than before entering the room? (x2 x 2) + (7x2 x) (h 8)2 = 0 Answer: -64 + 96 + 16 = 24 a. Given polynomial Describe a strategy for factoring the trinomial x2 + bx + c that does not use algebra tiles. 3s2 9s = 0 Answer: -2ab + 2b = y 2(3)(y) + 3 (y + 6)(y + 4) = y(y + 4) + 6(y + 4) Check your work by ite "prime." a 2 . There is an equivalent chance that the offspring receives a black or a white gene from each parent. -(2x + 2x + 3) \(\frac{5}{216}\)(x 72)(x + 72) = 0 Answer: Use the instructions below to start using our professional PDF editor: . Question 45. 4x2 = 2x Given, Answer: Answer: Answer: Answer: 22r 1 = 6x(x 2) + 1(x 2) m 2m + 1 MGSE9-12.A.SSE.3a (5y + 4) + (-2y + 6) You throw a water balloon from a building. 3m(3m 5n)(2m + n). (4c + 4d) = (4c) + (4d) + 2(4c)(4d) x 2(\(\frac{2}{3}\))x + \(\frac{2}{3}\) = 0 Answer: Writing a Product of Linear Factors Once we change this problem to an addition problem, we will use the horizontal method for solving it. 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