= (x + 1)(3x + 2), b. Answer: w2 4w + 3 Answer: We know its nice to share, but please dont share your membership content or your login or validation info. -2v = 0 or v + 1 = 0 (x 2)(x 3) = 0 Answer: Mathematically proficient students consider concrete models when solving a mathematics problem. = 8(k + 5k + 5k + 25) Answer: Question 12. A = (22 + 2x)(20 + 2x) Your friend says that if a trinomial cannot be factored as the product of two binomials, then the trinomial is factored completely. Answer: Question 48. Answer: in Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42 Answer: = x 4x + 6x 24 Answer: = x(x) + x(1) x(x) x(1) Question 1. b = -13, Question 20. b. Justify your answer. (2x + 1)(2x 1) = 4x 1, Question 7. A = (x + 1)(x + 1) (n 3)(n2 2n + 4) f + 5f + 12f + 8 y2 100 = y2 10 = (y + 10)(y 10), Question 33. Unit 2) Solving Equations and Inequalities. 6x4 + 8x2 = 26x3 Question 49. Question 32. y + 15y 2y 30 16x2 36 = 0 Number of terms = 3 5a(2a 3) + 1(2a 3) The coefficient is 2.8 and 1. The coefficient is 9. PLEASE RESPECT OUR COPYRIGHT AND TRADE SECRETS. Find the width of the entrance at ground level. x(x 3) 2(x 3) = 0 4x = 9 x + 8x 9x 72 = 0 x = 1 = x 1 = 0 Answer: Question 34. Question 4. MODELING WITH MATHEMATICS (x 4)(x + 2) = x(x + 2) -4(x + 2) x2 3x + 4ax 12a Use algebra tiles to factor each polynomial modeled by the tiles. 1. f(x) is a power function because it can be written as f(x) = 8x5. Step 2: Use factoring strategies to factor in the problem. (-12 n) = (-12) + n 2(-12)n LHS = RHS, Question 4. Question 5. = -2/315(x 315) 20 is less than 30 therefore the side of square is 50m. x(x + 3) + 5(x + 3) = 0 The second binomial is -8x 9, b. The area in part (a) is 81 square inches. y = (x + 1)(x + 7) Solve the system of linear equations by substitution. (z + 9)(z 2) Given, (2q 6)2 (2x 3x) (x2 2x + 4) d. (x 4)(x 5) = 0 8(4y 3) + 2(y 5) Area = length width Answer: Write the algebraic expression modeled by the algebra tiles. A = 2(20) 14(20) Explain your reasoning. Explain how you found your answer. b(b + 10) + 8(b + 10) = z(z 11) + 11(z 11) (n 3)(n2 2n + 4) m2 + 3m + 2 = 0 n 9 = 0 = 2k(k + 2) 9(k + 2) = 0 Why do you think it is called the Zero-Product Property? (p + 7) (6p2 + 13p) 0. y = 6 (24 + 2x)(16 + 2x) = 2(24)(16). when x = 21 So, (x + 1)(x2 + 5x + 8) = x + 6x + 13x + 8, Question 10. v(v + 13) 2(v + 13) = 0 The equation in part (b) of Exercise 47 on page 390 has two solutions. Answer: (c 3)(c 4) = 0 403408), Factor the polynomial completely. A web browser is open on your computer screen. If not, change the constant term so that the polynomial is a perfect square trinomial. b. Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30 c(c 3) 4(c 3) = 0 (x + 2) = x + 8 + 6x + 12x. y 2y 8 7 = 0 33 27 Factor out the common binomial. Get Form. -2y2 + 7y 6 Answer: Question 4. The x-axis represents the ground. Answer: Question 20. t = 0 or t = -2 Question 3. The Punnett square shows the possible gene combinations of an offspring and the resulting colors. A box in the shape of a rectangular prism has a volume of 72 cubic feet. Answer: a. Question 37. Math can be tricky, but there's always a way to find the answer. y 12y + 36 = 0 Answer: b. z 81 = z 9 29 = (30 1) z2 81 = 2d d + 12d + 7d 6d + 42 p 9 = 0 Wondering how to ace up your preparation for Chapter 7 Polynomial Equations and Factoring? Answer: y2 + 13y 30 The new area is 10,000 (10000 x) x Explain. MODELING WITH MATHEMATICS CRITICAL THINKING (b 3)(b 5) x + 9x x 9x = 72 x(6x + 8) = (26x)x (4s4 + 2st + t) + (2s4 2st 4t) (y + 4)(y + 1) a 3ab + b a + ab + b = 3(6v 5v 6) Answer: Question 50. y = 0 or y = 8 or y = -1/2 39x 17x 376 = 0 (x + y)(2x y) = 0 The patio will cost $10 per square foot. -x + 8 x2 9 = x2 3 = (x + 3)(x 3), Question 32. 72, 84 = 2x(x + 3) 1(x + 1) Answer: (x + 10)(x 10) = x (10) Interpret the coefficients of the polynomial in part (a). (7x 3) 33 27 = (30 + 3)(30 3) -4(x+ 2) Question 8. The volume of the box is 60 cubic inches. REASONING = 900 + 1 60 a(a + b) + b(a + b) 9x7 6x2 + 13x5 = 208, Factor the polynomial. g. x 4x = x(x 4) = x(x + 2)(x 2) F y = -2, 6. Easily fill out PDF blank, edit, and sign them. (m + 6)(m 6) Emath Instruction Inc.10 Fruit Bud LaneRed Hook, NY 12571. Will the invitation fi t in the envelope shown without being folded? Question 4. Answer: x = -22 or x = 15. The golf ball does not hit the pine tree. What is the balance of your account after 2 years? -3q4rs6 Answer: Example: Draw the rectangular array of algebra tiles that models each product of two binomials. Does the area of the parking lot increase, decrease, or stay the same? If you already have a plan, please login. PowerPoint is required to edit these files. s + 6s + 5s + 30 s + 8s 5s 40 How many times greater is the area of your pupil after entering the room than before entering the room? 8[(v + 3)(v 2)] What are the dimensions of the gift bag? y + 2y 3y + 9y + 18y 27 15x2 + 3x 8 = 5x 7 15x2 2x 1 = 0. What are the possible dimensions of the box? a. Answer: Question 36. n2 5n = 24 The expression 1000(1 + r )2 represents the balance after 2 years, where r is the annual interest rate in decimal form. y(y2 + 2y 3) + 9(y2 + 2y 3) Question 23. Question 27. Is there another method you can use to write the same polynomial? (y + 3)( y2 + 8y 2) (a b)= a + b 2ab Answer: 4m m + 2 + 3m 10m 4 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 f. (x 6)(x 1) = 0 7.4 Graphs of Polynomial Functions. 2k - 4. . Given, y = \(\frac{5}{216}\)(x 72)(x + 72) HOW DO YOU SEE IT? -2y2 + 7y 6 in These Terms & Conditions present some of the highlights of the Single User License Agreement in plain English, but its a good idea to look at the complete Single User License Agreement, too, because by checking the box below and proceeding with your purchase you are agreeing to both these Terms & Conditions and the Single User License Agreement. 3(s 1) + 5 2y3 12y2 + 18y S = -0.028(5)3 0.32(5)2 + 1.6(5) + 59 Write an expression that represents the length of the sign. 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. x 2x + 3x 6 A = P(1 + r/2)nt Answer: a. Which representation would you rather have when trying to solve for specific information? Answer: (x + 4)(x2 + 7x) It is in the form of (a + b) = a + b + 2ab = 4x + 1 + 4x x + 4x + 3x + 12 = x + 4x 32. Question 2. A = (x + 4)(3x) b. x(x + 3) 2(x + 3) Answer: x + 6x 5x 30 = 0 b 3b 5b + 15 = 0 y = -3x + 14x + 5 ac = pq Classify each polynomial by the number of terms. Answer: 7 5 = 35 Section 7.5 To Multiply Monomials with Polynomials Example 1: Simplify the followings. 2x(2x) + 2x(1) 1(2x) 1(1) Describe a strategy for factoring the trinomial x 2 + bx + c that does not use algebra tiles. Question 1. 10 m = (10 + m)(10 m), Question 3. x + 16x 25x = 0 Answer: (d 2)(d + 6)(d + 8) = 0 Area of the plot = 50 50 f. The opposite of 0 is equal to itself. Question 37. Without factoring, determine which of the graphs represents the function g(x) = 21x2 + 37x + 12 and which represents the function h(x) = 21x2 37x + 12. 3z2 + 26z 9 = 4x 1 16x2 169y2 A = (4c + 4d)(4c + 4d) It is in the form of (a + b)(a b) = a b \(\frac{1}{4}\)x + y = 9 The area of the invitation is 15 square inches. Write two polynomials whose sum is x2 and whose difference is 1. a. Step 4: 4x 3, Subtracting Polynomials Click on the respective link and kickstart your learnings. (y3 + 4) 03. Explain your reasoning. = (h + 2)(-8h + 3), Question 22. Question 3. y 7y 30 = 0 4x-5 = 4 or 3x = 9 Section 7.3 Factoring and Solving Polynomial Equations. Explain. = 273, Question 7. Multiplying Binomials4. y = -0.2(x + 22)(x 15) Question 1. b. x = 5, Question 8. Our state-specific browser-based blanks and complete instructions eliminate human-prone errors. x 2x + x 12x = 2x 14x = a(a + 3) + 1(a + 3) -3x2 x + 2 Question 41. x(x + 4y) + 2y(x + 4y) 7.3 Solving Polynomial Functions by Factoring. y2 + \(\frac{1}{2}\)y = 1 16 the y-intercept is 2. Please download the preview to see a sample outline along with a collage of some of the pages. So, 4r + 6 9r 1 = -5(r 1), Question 3. Answer: Question 42. A = \(\frac{3}{13}\) 24 = 104 sq. p(p + 7) 5(p + 7) c. The area of the trapdoor is 10 square feet. Question 8. This curriculum includes 900+ pages of instructional materials (warm-ups, notes, homework, quizzes, unit tests, review materials, a midterm exam, a final exam, and many other extras) for Algebra 1. Question 47. -3y( y 8)(2y + 1) = 0 (2x + 5)(x 2) The width of the patio is the same on every side. Question 12. = 4s4 + 2st + t + 2s4 2st 4t 5x2 5x 30 = 0 V = lbh Explain. Find the degree of the monomial. The Teacher-Author indicated this resource includes assets from Google Workspace (e.g. 3x(x 4) 2(x 4) If it is, find the degree and determine whether it is a . Answer: Answer: Question 46. So, (6x 3y) = 36x + 9y 36xy. Question 9. s 70s + 1000 = 0 e = E = 2, Writing a Conjecture width = 8 feet. a = 1/2 = c Question 12. x + 16 + 11x + 176 A = x(x 12) Factoring Special Products Work with a partner. = (3x) + (1) + 2(3x)(1) q = 0 or 9 = q It is in the form of (a b) = a + b 2ab Answer: In Example 5(a), how does the polynomial change when the longer base is extended by 1 foot? Answer: Question 26. WHICH ONE DOESNT BELONG? -2y2 5y 3 a) ( +4)2b) 7)2 c) (3 +4)2d) 5 1)2 Algebra 1 Unit 9 Notes: Polynomials and Factoring 8 v0 = 16 ft/sec w = 16 + 2x Level 1 is a rectangle having length x and breadth 10 + (x 12) x 5 = 0 or x + 3 = 0 x = 2 + 5 or x = 2 (x + 3)(x 2) = 2u + 3u + \(\frac{1}{2}\)u \(\frac{3}{4}\) 8a - 2. 2t5 + 2t4 144t3 = 0 The entrance of a tunnel can be modeled by y = \(\frac{11}{50}\)(x 4)(x 24), where x and y are measured in feet. 6x 7x 3 14x + 21x + 10x + 15 Answer: a. 48 = 24 (2) + 6(2) 4(2) = 24 Question 25. Answer: = 525, Question 8. 35 = g 19g + 88 b. Perfect SquareTrinomial Pattern, p. 399, Section 7.8 17 + 52 - 13x - 7 2. The sum of two polynomials is _________ a polynomial. So, (a + b)(a b) = a b Explain your reasoning. WRITING 2x x + 4x 2 n 8n + 3n 24 = 0 Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? (-3n2 + n) (2n2 7) = -3n + n 7, Question 7. x 11x 2x + 22 Question 3. = (5x) 1, Factor the polynomial. s(s 20) + 3(s 20) = 0 2x x = 15 x = -1, -8, Factor the polynomial. The area of the house after the renovation is represented by (x + 50)2. MODELING WITH MATHEMATICS It is in the form of (a + b)(a b) = a b a. w 3 = 0 or w 1 = 0 REASONING y 4x 1 Answer: Which polynomial does not belong with the other three? Answer: Question 54. Then nd the height of the object after 1 second. 9x7 6x2 + 13x5 A = (6 x) n2 12n + 35 2x(x + 1/2) = 10 (7m + 8n)(7m 8n) Answer: Graph the function. Simplify the expression. 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: 25x2 10x + 1 Answer: Question 50. = -7v 7v 12v 12 2k 9 = 0 or k + 2 = 0 a. x3 + 4x2 + 3x Question 7. 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. Answer: p + 30p + 225 The Punnett square shows the possible gene combinations of an offspring and the resulting colors from parents that both have the gene combination Na. a. (2d2 d + 7) h = 8, Question 14. 8(v + v 6) Please dont reverse-engineer the software or printed materials. Question 25. = 2p 4p 6, Question 34. Question 5. THOUGHT PROVOKING V = x + 16x. Go To; . ENGAGING. Which expression does not belong with the other three? (2 n) ( 6 + \(\frac{2}{3}\)n ) (n 2) = 0 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. Answer: x = 2 or x = 3 HOW DO YOU SEE IT? V = (4x 3)(x + 1)(x + 2) 25x 5x 5x + 1 What is its degree? Editing unit 7 polynomials and factoring answer key pdf online. I love the notes and the videos that go with it. (x + 3)(x + 5) = 0 It is in the form of (a b) = a + b 2ab 2w + 17w 16w 136 = 0 Given y = -16t2 + 24t (w \(\frac{7}{6}\)) = 0 x 25 = 0 x(x + 5) = 0 10w 31w + 15 = (2w 5)(5w 3), Question 14. -7y + y2 30 Each of two dogs has one black gene (B) and one white gene (W). Answer: Question 44. (x 4)(x + 2) Thats why we may do the following (and we ask that you agree): SATISFACTION GUARANTEED. s2 + 11s + 30 = (s + 6)(s + 5), Question 8. You may not pay any third party to copy and or bind downloaded content. The degree of a monomial is the sum of the exponents of the variables. 3t2 + 16t 12 Answer: 5x + 6x 5x 6 = 0 9r2 36r 45 It is in the form of (a + b) = a + b + 2ab Combine the like terms to add or subtract the polynomials (-2p + 4) (p2 6p + 8) 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. Answer: Given, m = y2 y1/x2 x1 Add 6x5 10x2 +x 45 6 x 5 10 x 2 + x 45 to 13x29x +4 13 x 2 9 x + 4. Write a polynomial that represents the area of the golf hole. y = \(\frac{2}{315}\)(x + 315)(x 315) We are a small, independent publisher founded by a math teacher and his wife. D. 2x3 24x 2 The name of the polynomial is trinomial. (2x + 7)(2x 7) = 0 Question 9. p + 7 6p2 + 13p Answer: 7 6 = 42 -3n2 + n 2n2 + 7 (b + 7)2 = 0 4x(x 1) 1(x 1) A = x 12x x2 + 7x + 6 = -p 2p + 6p + 4 8 -8t = 0 or 2t 3 = 0 9 8 F 12 7 E 3 U 6 E : T 8 5 T 7 U E 14 6 ; 3 2(x 1) + 3(x + 2) Check your answers by FOIL. The degree of the polynomial is 6 (4 b)(5b2 + 5b 4) p2 + 2p 35 y = 61x 61 + 62 (x 1)(x 1)(x 2)(x 3) = 0. x = 1, 2 y2 + 13y + 40 (w 4)(w 4) = 0 a. (-x2 + 9xy) (x2 + 6xy 8y2) Given expression Answer: x = 3 = x 3 = 0 -28r = 4r2 p + p + 3 + 4p + p 3 x = 3, 4 Write the polynomial in the factored form using the dimensions of the rectangle. (x2 + 2x 1) + (2x2 2x + 1) (x + 1)(x + 4), c. x 7x + 12 Question 43. m2 2m + 1 -5y 20y 2y 8 MAKING AN ARGUMENT Essential Question How can you use algebra tiles to factor the trinomial ax2 + bx + c into the product of two binomials? How does this value relate to the graph? = m 10m + 21 3x 13x + 4 = 0 392 362 WHY. -7y + y2 30 Describe a strategy for factoring the trinomial x2 + bx + c that does not use algebra tiles. Answer: Answer: Answer: = 10000 21 20x3 + 30x2 8v2 + 8v 48 r(r 10) = 0 V = lbh Answer: = (5x + 1)(5x + 1) (x 1)(3x + 1). (2x + 7) = 4x + 49 + 28x, Question 14. (z + 3)(z 25) = 0 Work with a partner. 2k + 4. k + 4. f(x) = 2(3)x 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9. Given, The product of given numbers must be zero, so it is called zero product property. (r3 6t4)(r3 + 6t4) Is your friend correct? Given polynomial (-2p + 4) (p2 6p + 8) s 17s 60 = 0 (-3n2 + n) (2n2 7) 2b + 1 = 0 or 7b 2 = 0 = 9559 sq. Answer: t = 0 or t = 3/2 Compare factoring 6x2 x 2 with factoring x2 x 2. (m 3)(m 7) = m 10m + 21, Question 6. = 4x + 120x + 3456, c. Find the perimeter and the area of the blanket including the fringe when the width of the fringe is 4 inches. = 2y(y 3), Question 5. s 50 = 0 or s 20 = 0 8a - 2. a c = 0 Question 11. x 1x 2x + 2 Mediation is a faster and less formal way of resolving disputes and therefore tends to cost less. So, d = 1/2, -1/2, Question 16. Answer: (-3p3 + 5p2 2p) + (-p3 8p2 15p) x = 72 or x = -72 \(\sqrt{4}\) = 2, Question 52. -5m2 + 6m 1 Answer: Question 16. = (5 + 2x)(5 2x), Question 8. (x + 9)(x 9) = 2x + 1, Question 3. = -8h 16n + 3n + 6 Answer: (y + 9)(y2 + 2y 3) 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). Question 41. Answer: Question 48. w 2. y = 30/5 h = 12 in. k + 25 does not belong with the other three. So, x = 0, -5, Question 18. (t 2)(t2 5t + 1) Question 1. y = 9 (\(\frac{1}{3}\))x Your data is well-protected, because we adhere to the most up-to-date security requirements. (x x)(x + 9) = 72 = 7b(2b + 1) 2(2b + 1) = 0 s\(\frac{3}{13}\) = 104 in\(\frac{3}{13}\) 1. x2 - 36 2. a2b2 - 100 3. A = P(1 + r/2)nt a. a. Use your methods in Question 3 to find each sum or difference. v2 + 11v 26 = 0 Work with a partner. In parts (c) and (d), first draw the rectangular array of algebra tiles that models each product. 4x + 25x 56x = 0 REASONING Answer: Question 44. This Polynomials and Factoring Unit Bundle contains guided notes, homework assignments, three quizzes, a study guide and a unit test that cover the following topics: Multiplying Binomials (FOIL) and Binomial x Trinomial, Factoring by finding Greatest Common Factor (GCF), Factoring Trinomials (ax2 + bx + c) *By Slip & Slide, Factoring Review (organized by type, then practice with it mixed), Dividing Polynomials by a Binomial (by Factoring). Question 47. 0. HOW DO YOU SEE IT? 4x + 12x 216 = 0 When is it not possible to factor ax2 + bx + c, where a 1? k2 10k + 24 = z 121. x(x 1)(x + 9) = 72 WHAT IF? (-p2 + 4p) (p2 3p + 15) a. w2 + 18w + 84 (t + 5)2 HOW DO YOU SEE IT? (3) Google Slides Version of the PDF: The second page of the Video links document contains a link to a Google Slides version of the PDF. d2 + 14d + 49 = 0 b. The combined length is equal to the sum of lengths of the photo and the frame. b. Answer: Question 54. 3h2 + 11h + 6 (x 1)(x 2) = 0 Question 21. 8x2 56x + 48 Answer: (y + 6)(y + 4) a. Show how you could use a polynomial to model the possible gene combinations of the offspring. MODELING WITH MATHEMATICS n = 2 or n = -9 or n = 2 Use algebra tiles to write each polynomial as the product of two binomials. = -8x + 9x 12 + 4 Answer: n = 2 or n = -18/2 or n = 2 A = 1000(1.03) 3 + 3 = 6 e. When you multiply a number n by 0, you get 0. Polynomial is trinomial tiles that models each product 14x + 21x + 10x + answer! 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