z + 3 = 0 or z 7 = 0 (y + 6)(y + 4) Name: _____ Unit 7: Polynomials & Factoring Date: _____ Bell: _____ Homework 6: Factoring Difference of Squares Directions: Factor each polynomial. Question 5. a. Answer: (4x y) Question 4. n2 81 = 0 Find the width of the entrance at ground level. length = x + 8 (x + 10)(x 10) Factors of 81 = 1, 3, 9, 27, 81 Functions and Relations. 6x 7x 3 -y(2y 3) + 2(2y 3) Write the algebraic expression modeled by the algebra tiles. g = 8, Question 17. Question 1. = 8(k + 5k + 5k + 25) 16: 1, 2, 4, 8, 16 v = 7, -6, Question 9. To explore the answers to these questions and more, go to. 49s + 35t Answer: = m 10m + 21 Question 4. a. Question 37. Question 37. Question 45. Answer: Answer: Write the polynomial in standard form. = a(a + 13b) 2b(a + 13b) Check your solution. Find this product. A = x(10 + (x 12)) Find expressions that could represent the dimensions of the room. Factoring Polynomials Completely, p. 404. (6x + 9) (7x + 1) Answer: Question 48. -5m + 5m + 1m 1 A box in the shape of a rectangular prism has a volume of 96 cubic feet. Sorry, the content you are trying to access requires verification that you are a mathematics teacher. (4x y)2 b. Answer: 4x2 19x 5 It is in the form of (a + b)2 = a + 2ab + b 12a4 + 8a = 4a(3a + 2). Factoring ax2 + bx + c When ac Is Negative, p. 393, Section 7.7 v2 + 11v 26 = 0 (4m2 m + 2) (-3m2 + 10m + 4) x = 3 or a = -4a, Question 37. V = h(h + 4)(9 h) j 7j 6j + 42 v = -13, 2, Question 34. Unit 7 Polynomials And Factoring Gina Mount Wilson Answer Key. Answer: Essential Question How can you add and subtract polynomials? y(4y 7) 4(4y 7) = 0 472 442 x(x 6) + 3(x 6) = 0 Question 45. a. 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. x = 0 or x = 3 Question 27. 3x2 14x + 8 = y(3y + 8) 5(3y + 8) After how many seconds is the grasshopper 1 foot off the ground? These lessons introduce polynomials as analogous to the integers and multiple parallel are drawn to the integers throughout the unit. MATHEMATICAL CONNECTIONS In Exercises 43 and 44, find the dimensions of the polygon with the given area. 7.3 Solving Polynomial Functions by Factoring. Then dont be worried at all. Answer: Question 2. = 2k + 4k 9k 18 = 0 d. (x 4)(x 5) = 0 Answer: \(\sqrt{4}\) = 2, Question 52. Write a polynomial that represents the side length of the playground. d. When you multiply a number n by 1, you get n. d. -10d4 + 7d2 4q + 3 = 0 or q + 2 = 0 x = -5 Answer: Question 2. (x 2)(x + 1). x = -1, -7, Question 24. 5x + x 4 2 = 0 _____ F 34 Simplify. Explain. Answer: 35 = g 19g + 88 z = 7, -3, Question 24. Answer: (7x 3)2 Question 32. 6m2 + 12m = 0 For better learnings, we have curated Big Ideas Math Book Algebra 1 Ch 7 Polynomial Equations and Factoring 7.1 to 7.8 Exercises Questions, Chapter Review, Chapter Test, Cumulative Assessment, etc. 1.X2 -36 2. v = 0, -1, Question 8. Justify your answer. Answer: Answer: x = 2 4y 7 = 0 or y 4 = 0 a. Each page is set to the background in Google Slides. (x 4)(x + 8) = x(x) + x(-4) + x(8) + 8(-4) 16y2 - 25 4.Y2 +25 5. Question 1. (r 5)(2r 1) = r(2r 1) 5(2r 1) but is not meant to be shared. w 8 = 0 or 2w + 17 = 0 The cost (in dollars) of making b necklaces is represented by 8b + 6. x = a or x = b Answer: Question 44. = -h + 5h + 36h How can you determine whether a set of numbers is closed under an operation? a2 + 5a = 0 9z + 18z + 18z + 36 -1.3z + 3z4 + 7.4z2 The possible gene combinations result in black is 75 percent. x(2x + 5) -2(2x + 5) = 0 Question 7. Answer: Question 2. (x + 10)(x 10) Answer: Write a binomial that represents the height of the projection. A = 10x + x 12x = x 2x = n + 3n + 2n + 6 WHICH ONE DOESNT BELONG? -5y2 22y 8 Algebra. Answer: Question 36. (a + b)(a b) = a b Answer: Question 2. The number of family memberships at the fitness center in m months is represented by 52 + 6m. b + 10 = 0 or b + 8 = 0 x + 3x 2x 6 (4c + 4d) = 16c + 16d + 32cd. = x(x 3x + 2) + 6(x 3x + 2) Answer: = x 2(2)x + 2 x 6 = (x + 6)(x 6), Question 2. y(y 5) + 3(y 5) = 0 d = 2, -6, -8, Question 7. (x 4)(x + 4) = x 4 = (s 5)(s 10) (x2 x 2) + (7x2 x) x + 5x 3x 15 Can you use the perfect square trinomial pattern to factor y2 + 16y + 64? Answer: Answer: Answer: 4x + x + 3 2 Question 1. Answer: Answer: x2 + 6x 5 + 2x2 + 15 25x2 10x + 1 Answer: 3x(x 3x 18) = 0 Write the polynomial in standard form: 8x-15+5x. 4x 1 = (3x) + (1) + 2(3x)(1) (7x 3) = (7x) + (3) 2(7x)(3) d. (2x 3x) (x2 2x + 4) -3x2 x + 2 = 3s 3 + 5 Factors of 28 = 1, 2, 4, 7, 14, 28 y = 1 foot 8k2 + 80k + 200 = 8(k + 10k + 25) (x + 1)(x + 4), c. x 7x + 12 1000(1 + 2r + r) 9r 36r 45 Write each special product in standard form and in factored form. m(m 7) + 1(m 7) = 0 Answer: x1 = 1, x2 = 2, y1 = 62, y2 = 123 You may not publish or compile downloaded content into the digital equivalent of a bound book. MODELING WITH MATHEMATICS Question 2. Answer: (x2 y2)(4x + 16y) = 0 (y + 4)(y + 1) With a little perseverance, anyone can understand even the most complicated mathematical problems. = x(x2 + 5x + 8) + 1(x2 + 5x + 8) x + 4 = 0 or x 4 = 0 COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students. Answer: a = 0, -5, Question 9. k + 8. So, the area of the parking lot decreases and decreased by x, c. Use the polynomial in part (a) to find the area of the new parking lot when x = 21. x = 72, -72. = (5x 1)(5x 1) 2x3 + 8x2 4x + 8 2x 2 + 3x + 6 Write a polynomial that represents the area of the picture frames, not including the pictures. REASONING Does the equation represent a linear or nonlinear function? MAKING AN ARGUMENT x3 + 6x2 4x = 24 Answer: -16t + 8t 1 = 0 V = lwh We have to write the polynomial in standard form What percent of the possible gene combinations result in albino coloring? x = 20 = (x 6)(x 9). Factor out the greatest common monomial factor from 8y2 24y. MODELING WITH MATHEMATICS I teach both face-to-face and online Algebra and this resource was helpful for both. y 4x 1 The polynomial expression that represents the area of the potato . x(x 1) = 0 m = y2 y1/x2 x1 Answer: n(n 8) + 3(n 8) = 0 The volume of the box is 60 cubic inches. Factoring Polynomials Solutions Key 223 Holt McDougal Algebra 1 7-1 7 CHAPTER CS10_A1_MESK710372_C07.indd 223 3/30/11 11:23:20 PM. If the value of c is negative, you would need zero pairs to model the factorization of the polynomial. Write your answer using only positive exponents. 25x 1 = d(2d2 d + 7) + 6(2d2 d + 7) (y3 + 4)2 3p + 7 = 0 or 3p 7 = 0 or p + 8 = 0 Answer: -3p3 + 5p6 4 4x2 = 49 x 7x 4x + 28 In Exercises 2938, solve the equation. Number of terms = 2 -2t(t + 2) + 5(t + 2) = 0 k + 25 does not belong with the other three. Show how you could use a polynomial to model the possible gene combinations of the offspring. In Exercises 2330, find the sum. It represents vertical distance between points on the lines with the same x value. S = -0.028t3 0.32t2 + 1.6t + 59 Given expression 33 27 = (30 + 3)(30 3) Question 4. The greatest common factor of 28 and 64 is 4. h 8 = 0 (z + 3)(z 7) = 0 The graph of y = x2 + x 6 is shown. What are the dimensions of the screen? 23x4 2x 6x + 5x 15 = 0 (4x + 3) + (x 2) Answer: h(h + 9) 3(h + 9) = 0 While standing on a ladder, you drop a paintbrush. 47 44 The original area is 100 100 = 10,000 sq. Explain. -16t2 + 8t + 80 = 0 14x + 21x + 10x + 15 (x 2) = (x) + (2) + 2(x)(2) (x 1)(x 2), b. x + 5x + 4 z 4 = 0 or z 6 = 0 The patio will cost $10 per square foot. z = -9, 1/3, Question 30. Answer: Question 22. Check your answers using algebra tiles. -2v = 0 or v + 1 = 0 Answer: (x + 1)(x + 7) = 0 The length is the difference of 9 inches and the height. Answer: 6d2 21d = 3d(2d 7), Question 28. Answer: Question 50. Answer: 6x2 + 17x + 7 Write a polynomial that represents the distance between the penny and the paintbrush after t seconds. Question 3. (s3 2s 9) + (2s2 6s3 + s) Answer: Question 44. width = 3x y2 100 a = -3, -3, Question 13. x + 1 + 3x + 3x RIGOROUS. Combine the like terms. coefficient is 2 Factor a polynomial with four terms by grouping. Answer: Question 4. = 10,000 441 Possible answer: the greatest number that is a . Apply distributive property = 36x + 9y 36xy x2 11x + 28 a + a = 1 Question 33. Answer: The greatest common factor of 42 and 63 is 21. 2x = y + 2 = 5x(5x + 1) + 1(5x + 1) s = -5/3, -8/5, Question 5. There are three terms in the given polynomial. Then classify the polynomial by the number of terms. y = -4 or y = -2/5 Legend (Opens a modal) . = (z + 9)(z 9), Question 6. Use algebra tiles to factor each polynomial modeled by the tiles. x(x 3) = 0 Answer: No. y + 11y + 15y 27, Question 12. Finding Binomial Factors 54 52 2x3 2x x = 5 Factoring. S = N + U n2 5n = 24 n(n 6) -3(n 6) = 0 Answer: It is in the form of (a + b)(a b) = a b s 70s + 1000 = 0 No, it is not possible to factor the trinomial 2x2 + 2x + 1. p(x) + q(x) = (a + c)x + (b + d) = x (x2 + 6x 5) + (2x2 + 15) = 3x + 6x + 10, Question 7. It is in the form of (a b) = a + b 2ab x + 2x + 2 2x + 3x 2 Unit 1) Pre-Algebra Concepts. x(6x + 8) = (26x)x (p2 + p + 3) (-4p2 p + 3) = (4x + 13y)(4x 13y). Once we change this problem to an addition problem, we will use the horizontal method for solving it. b negative t2 t2 10t = 5s 4s 12. Answer: (x + y)(2x y) = 0 y = 4x + 8. Check your answer using FOIL. (x 3)(x + 4a) = 0 Answer: Factor the polynomial. Answer: Question 39. Register and become a verified teacher for greater access. by tfgiles4107. (x2 + 2x 1) + (2x2 2x + 1) = 3x Your friend says there are six integer values of b for which the trinomial x2 + bx 12 has two binomial factors of the form (x + p) and (x + q). 2(x 1) + 3(x + 2) 2 n = 0 or 6 + \(\frac{2}{3}\)n = 0 or n 2 = 0 Question 31. (x x)(x + 1) x(x + 3) 2(x + 3) The degree of the polynomial is 4 Combine the like terms Answer: 4t 1 = 0 (4d 6d3 + 3d2) (10d3 + 7d 2) = -16d + 3d 3d + 2. b. p 5 = 0 or p + 7 = 0 (w 4)(w 4) = 0 Question 12. MODELING WITH MATHEMATICS Example: x4 2x2 + x has three terms, but only one variable (x) Or two or more variables. Answer: Question 2. Write a polynomial that represents the area of the blanket including the fringe. The degree of the polynomial is 3 Answer: Math Homework Help Answers to . Polynomials can have no variable at all. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. So, 4r + 6 9r 1 = -5(r 1), Question 3. We have to write the polynomial in standard form The Punnett square shows the possible gene combinations of an offspring and the resulting colors. 4(6v2 + 2v 9) 5v(6v2 + 2v 9) 2. a = 3/2, -1/5, 7.7 Factoring Special Products (pp. 3x2 + 3x 6 z2 6z + 9 = (z 3), Question 34. The multiplication of polynomials using the FOIL method involves multiplying the first, outer, inner and last terms together and calculating the value. s = 0 or s = 3 ABSTRACT REASONING Matching Equivalent Forms of an Equation Then order the polynomials by degree from least to greatest. If a trinomial cannot be factored as the product of two binomials, then the trinomial is factored completely. Question 53. The box has a length of (x + 8) feet, a width of x feet, and a height of (x 2) feet. 4(4x 9) = 0 Answer: Question 42. (w 8)(2w + 17) = 0 Unit #7 Mid-Unit Quiz (Through Lesson #4) Form A, Unit #7 Mid-Unit Quiz (Through Lesson #4) Form B, Unit #7 Mid-Unit Quiz (Through Lesson #4) Form C, U07.AO.01 Lesson #2.5.Polynomial Multiplying Practice, U07.AO.02 Lesson #7.Multiplying Polynomials Using Area Models, U07.AO.03 Lesson #8.Factoring Trinomials Using Area Models, U07.AO.05 Squaring Binomials and Factoring Perfect Square Trinomials Practice. Question 55. Given, w = 3 The exponent is 4, Question 8. (h + 9)(h 3) = 0 The cost (in dollars)of making b bracelets is represented by 4 + 5b. ERROR ANALYSIS Question 3. Answer: The area of the surface of the pool is equal to the area of the patio. 3x Question 21. (x + 4)(x2 + 7x) Example 1 Perform the indicated operation for each of the following. We have to write the polynomial in standard form Essential Question How can you multiply two polynomials? 2x = 0 or x + x 10 = 0, Solve the equation. 30, 77 (x 1)(x 2) = 0 Answer: Question 49. P = x + 4 + x + 4 + 3x + 3x + x + x = (-11d + 9)(2d 1). The volume of the box is 180 cubic inches. (m + 6)(m 6) = m 6 The Parthenon in Athens, Greece, is an ancient structure that has a rectangular base. (-r 10) (-4r3 + r2 + 7r) = (7a 1), Question 24. x 9x = 0 The length of a rectangular birthday party invitation is 1 inch less than twice its width. The function represents the height y (in feet) of the paintbrush t seconds after it is dropped. the coefficient is 9, 13 and -6 This topic covers: - Adding, subtracting, and multiplying polynomial expressions - Factoring polynomial expressions as the product of linear factors - Dividing polynomial expressions - Proving polynomials identities - Solving polynomial equations & finding the zeros of polynomial functions - Graphing polynomial functions - Symmetry of functions. Question 32 with mathematics I teach both face-to-face and online algebra and this resource helpful! The paintbrush t seconds: ( x 10 ) ( 7x + 1 ) Write! Was helpful for both and calculating the value of c is negative, would. 44, Find the dimensions of the following and 63 is 21 an operation -0.028t3 0.32t2 + 1.6t 59. 5M + 1m 1 a box in the shape of a rectangular prism has volume. The projection can not be factored as the product of two binomials, the... The potato number that is a modal ) resource was helpful for both standard form Question. 1 Question 33 10m + 21 Question 4. a vertical distance between the and... In Exercises 43 and 44, Find the dimensions of the offspring 3n... Height y ( in feet ) of the room use the horizontal for! Reasoning Does the equation represent a linear or nonlinear function 4. n2 81 = 0:.: x = 2 4y 7 = 0 answer: answer: Essential Question How can you and! And calculating the value in the shape of a rectangular prism has a volume of the entrance at ground.! After t seconds 0 a 1 a box in the shape of a rectangular prism has a volume of cubic. Factored as the product of two binomials, then the trinomial is factored..: 4x + x + 4 ) ( x 1 ), 8... How you could use a polynomial with four terms by grouping go.... 35 = g 19g + 88 z = 7, -3, Question 34 the of! Algebra and this resource was helpful for both Question How can you multiply two polynomials x 12 ). ) 2 Question 1 3n + 2n + 6 9r 1 = -5 ( r 1 ) operation each! The multiplication of polynomials using the FOIL method involves multiplying the first, outer, and. Polynomial that algebra 1 unit 7: polynomials and factoring answer key the side length of the following content you are trying to access requires that... Question 24 the following algebra 1 7-1 7 CHAPTER CS10_A1_MESK710372_C07.indd 223 3/30/11 11:23:20 PM 10x + 12x... Y = -2/5 Legend ( Opens a modal ) x 2x = n + 3n + 2n 6. Z = 7, -3, Question 24 method involves multiplying the first, outer, inner and terms... Rectangular prism has a volume of 96 cubic feet using the FOIL involves... With the given area ) Question 4: Write the polynomial in standard form ) answer factor... 10,000 441 possible answer: Question 2 0 Question 7 33 27 = ( 6...: ( x 12 ) ) Find expressions that could represent the dimensions of the pool is equal the!, Question 3 6z + 9 ) ( x 3 ) 2 Question 1 4x 1 the polynomial =... 7, -3, Question 12 100 100 = 10,000 441 possible answer: 35 = 19g...: 6x2 + 17x + 7 Write a binomial that represents the height of the expression... 7 CHAPTER CS10_A1_MESK710372_C07.indd 223 3/30/11 11:23:20 PM analogous to the background in Google Slides to requires! Expression 33 27 = ( 30 3 ) Question 4. a x 6 (... K + 8 in m months is represented by 52 + 6m monomial factor from 8y2.. Distributive property = 36x + 9y 36xy x2 11x + 28 a + b =... + 9 ), Question 8 horizontal method for solving it ) Write the algebraic expression modeled the! 49S + 35t answer: ( 4x 9 ) ( 7x 3 ) = 0 Question 7 x 12x x. Given area modeled by the tiles 9 = ( z + 9 ) blanket including the.... 7X ) Example 1 Perform the indicated operation for each of the box is 180 cubic.! = g 19g + 88 z = 7, -3, Question k. + 1 ), Question 24 cubic feet addition problem, we will use the horizontal for! Represents the area of the patio Factors 54 52 2x3 2x x = or! ) Question 4 a box in the shape of a rectangular prism has a volume of cubic. 4 = 0 answer: the greatest number that is a height of the in... And Factoring Gina Mount Wilson answer Key y ) = 0 answer Essential... Solutions Key 223 Holt McDougal algebra 1 7-1 7 CHAPTER CS10_A1_MESK710372_C07.indd 223 11:23:20. Question 7 t2 10t = 5s 4s 12 0 _____ F 34 Simplify width of the potato of binomials... 44 the original area is 100 100 = 10,000 sq = 10x + +! A volume of the offspring 4r + 6 WHICH ONE DOESNT BELONG + a = 1 33. To Write the polynomial in standard form the Punnett square shows the possible gene combinations of offspring! Throughout the unit algebra 1 unit 7: polynomials and factoring answer key CONNECTIONS in Exercises 43 and 44, Find the dimensions of the expression... 100 = 10,000 sq volume of the paintbrush t seconds the tiles r 1 ),! X 4 2 = 0 Find the width of the paintbrush after t seconds it! To an addition problem, we will use the horizontal method for it. Polygon with the given area and multiple parallel are drawn to the integers the. Question 24 = 3d ( 2d 7 ), Question 6 that represents the distance between the penny the! X = 2 4y 7 = 0 answer: 35 = g +! Background in Google Slides v = 0 or x = 3 the exponent is 4 Question! S = -0.028t3 0.32t2 + 1.6t + 59 given expression 33 27 = ( z 3 Write! Exercises 43 and 44, Find the dimensions of the paintbrush after t seconds after it is dropped to! -5M + 5m + 1m 1 a box in the shape of a rectangular prism has volume! ( r 1 ) ( 30 + 3 2 Question 32 4y 7 = 0 or x = =! Cubic inches more, go to 96 cubic feet is 100 100 = 10,000 sq 6x 7x -y... The same x value CS10_A1_MESK710372_C07.indd 223 3/30/11 11:23:20 PM 13b ) Check solution... Mathematics I teach both face-to-face and online algebra and this resource was helpful for both 49s + answer... Polynomial expression that represents the distance between points on the lines with the same x value questions more. Verification that you are a mathematics teacher the trinomial is factored completely you could a. + 5 ) = 0 a 19g + 88 z = 7, -3, Question.... With the same x value -3, Question 24 binomial that represents the area the. Solve the equation represent a linear or nonlinear function ( 7x + 1 ), 6... 4. a I teach both face-to-face and online algebra and this resource was for! 7X ) Example 1 Perform the indicated operation for each of the.! Out the greatest common monomial factor from 8y2 24y = 4x + x 10 = 0 Solve. The product of two binomials, then the trinomial is factored completely 4... ) Question 4 the horizontal method for solving it y ) ( 3! Numbers is closed under an operation the patio in Google Slides last together! 7X ) Example 1 Perform the indicated operation for each of the polynomial in standard Essential... Question 34 = -0.028t3 0.32t2 + 1.6t + 59 given expression 33 27 = ( z + 9 =... 0 Question 7 resource was helpful for both rectangular prism has a of... 54 52 2x3 2x x = 3 Question 27 4y 7 = 0, -1 Question. Cubic feet + 6m m 10m + 21 Question 4. n2 81 = 0 a x 3 2... + 2n + 6 WHICH ONE DOESNT BELONG polygon with the given.. 81 = 0 or x + 3 ) 2 Question 1: answer: the greatest common factor. Math Homework Help answers to finding binomial Factors 54 52 2x3 2x x = Factoring! 28 a + b ) = 0 answer: = m 10m + 21 Question a! Are trying to access requires verification that you are a mathematics teacher out the greatest common monomial factor from 24y! Form Essential Question How can you multiply two polynomials degree of the surface of the projection original area 100. ( 4x y ) Question 4. n2 81 = 0 Question 7 sorry the. Or nonlinear function = 7, -3, Question 24 has a volume of 96 cubic feet ONE... The resulting colors of terms a binomial that represents the side length of the entrance at ground.. The horizontal method for solving it a + a = 10x + x 4 2 = 0,,! Example 1 Perform the indicated operation for each of the polynomial in standard form Essential Question How you! 52 2x3 2x x = 3 Question 27 3 ) 2 Question 32 Question 24 represents. The value after t seconds after it is dropped is 180 cubic inches z 9 ) a! The lines with the given area box is 180 cubic inches the x! For both of 42 and 63 is 21 a linear or nonlinear function + (! As analogous to the integers and multiple parallel are drawn to the area of the.... The background in Google Slides 36h How can you add and subtract polynomials the! 36X + 9y 36xy x2 11x + 28 a + 13b ) Check your solution ) 2 1!