Get Ready. 6. Expand using the distributive property. a) 6m(2m 4) b) 8xy(2x y) c) 6a 2 ( 3a + 4ab) d) 2a(b 2 6ab + 7)

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1 Get Ready BLM Classify Polynomials 1. Classify each polynomial by the number of terms. 2y x 2 + 3x + 2 c) 6x 2 y + 2xy + 4 d) x 2 + y 2 e) 3x 2 + 2x + y 4 6. Expand using the distributive property. 6m(2m 4) 8xy(2x y) c) 6a 2 ( 3a + 4a d) 2a(b 2 6ab + 7) 7. A rectangular prism has the dimensions shown. 2. State the degree of each polynomial. x 2 + 3x 1 x + 2y + 4z c) 6 + 2y 3 + xy d) 7a 3 b 2 + 6a 2 b 2 7ab Add and Subtract Polynomials 3. Simplify. (3x + 7) + (3x 6) (2a + (6a 4 c) (3x 2 + 2x 4) (2x 2 5x + 1) d) (9y 3 7y 2 + 4) (3y 3 + 2y 2 1) 4. Simplify. (6x 2 + 2xy 3y 2 ) + (8x 2 4xy 2y 2 ) (8ab 2 + 8a b 2 ) (9ab 2 7a + b 2 ) c) (6x 8) (4x + 7) + (6x 2) d) (6a 2 + (2b 3a 2 ) (11b 2 + 9a 2 + 2) The Product of a Monomial and a Polynomial 5. Expand using the distributive property. 2x(x + y) 8(6a 2 4 c) 6(a + 7) d) 2(3x 2 + 2x + 4) Find a simplified expression for the volume. Find a simplified expression for the surface area. Factors 8. Write all of the factors of each number c) 17 d) Write each number as the product of prime factors c) 40 d) 55 BLM 5 1 Get Ready

2 Section 5.1 Practice Master BLM What binomial product does each model represent? 5. Expand and simplify. 2(x 7)(2x + 1) (x + 3)(x + 6) 2(x + 1) c) (x 4)(x 1) + 5(3x 1)(2x + 1) d) (m 2) 2 (3m + 2) 2 e) (m + 7)(m 1) + 4(2m + 1)(3m 4) f) 6(2x + 1)(6x + 1) + 3(4x 3) 2 6. Write and simplify an expression to represent the area of each shaded region. 2. Model each product using algebra tiles, virtual tiles, or a diagram. 3x(x + 3) (x + 3)(x + 2) c) (x + 1)(2x + 1) 3. Use the distributive property to find each binomial product. (x 2)(x + 3) (y + 6)(y + 2) c) (n + 4)(n 5) d) (d + 6)(d + 7) e) (x 8)(x 6) f) (a 6)(a 3) 4. Use the distributive property to find each binomial product. (x 2y)(x + 2y) (2x + 1)(x 3) c) (k 6)(k + 7) d) (2p 7q)(2p 5q) e) (3 2s)(2 3s) f) ( 2t r)( 3t + r) 7. A rectangular prism has a width of x centimetres. Its length is 4 cm more than its width and its height is 5 cm more than its width. Draw a diagram of the prism. Write a simplified expression for the volume of the prism. c) Write a simplified expression for the surface area of the prism. BLM 5 3 Section 5.1 Practice Master

3 Section 5.2 Practice Master BLM Draw a diagram to represent each product. (x + 3) 2 (x + 2) 2 2. Expand and simplify. (x + 4) 2 (y + 7) 2 c) (a + 8) 2 d) (q + 5) 2 3. Expand and simplify. (3y + 6) 2 (3x + 2y) 2 c) (2x + y) 2 d) (6c + 7d) 2 4. Expand and simplify. (x 6) 2 (b 25) 2 c) (r 11) 2 d) (e 7) 2 5. Expand and simplify. (8a 1) 2 (2u 3v) 2 c) (6p 7) 2 d) (5q 8r) 2 6. Expand and simplify. (v 2)(v + 2) (x + 6)(x 6) c) (x + y)(x y) d) (r s)(r + s) 7. Expand and simplify. (6g 7h)(6g + 7h) (3x + y)(3x y) c) (g 9x)(g + 9x) d) (4x 5y)(4x + 5y) 8. A cube has length, width, and height of x metres. Each dimension is increased by y metres. Write a simplified formula for the volume of the new cube. Write a simplified formula for the surface area of the new cube. 9. A parabola has equation y = (x 3) 2. Identify the coordinates of the vertex. Expand and simplify the equation. c) Verify that the coordinates of the vertex satisfy your equation from part. 10. The side length of a square is represented by x centimetres. The length of a rectangle is 3 cm greater than the side length of the square. The width of the rectangle is 3 cm less than the side length of the square. Which figure has the greater area and by how much? 11. Expand and simplify. (4x 2 + 3y 2 ) 2 (3x 2 + 2y 2 )(3x 2 2y 2 ) c) (x 3) 2 (x + 3)(x 3) d) 3(2b + 1)(2b 1) + (b 3) 2 e) (3x 2 + 5x 1) 2 f) (2x 3) 3 BLM 5 4 Section 5.2 Practice Master

4 Section 5.3 Practice Master BLM Use algebra tiles or a diagram to illustrate the factoring of each polynomial. x 2 + 3x 2x x c) 3x 2 + 6x 2. Factor fully. 3x + 6y 17ac 34ad c) 16x 2 y 2 24xy d) 27x 3 y x 2 y 2 + 9xy e) 6n 2 p np n 3 p 3 f) 33c 4 d 3 e 2 11c 2 de g) 3g 2 + 6g Factor fully. 2x(x + 7) + 3(x + 7) a(b 7) + 2(b 7) c) 4s(r + u) 3(r + u) d) y(x + s) + z(x + s) 6. Factor. 3x(6 y) + 2(y 6) 2y(x 3) + 4z(3 x) 7. Write an expression in factored form for the area of each shaded region. 4. Factor by grouping. ax + ay + 3x + 3y 4x 2 + 6xy + 12y + 8x c) y 2 + 3y + ay + 3a d) 25x 2 + 5x + 15xy + 3y 5. The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh. Write this formula in factored form. If l is 10 cm, w is 5 cm, and h is 8 cm, find the surface area using both the original formula and the factored form. What do you notice? Explain why this is so. BLM 5 6 Section 5.3 Practice Master

5 Section 5.4 Practice Master BLM Illustrate the factoring of each trinomial using algebra tiles or a diagram. x 2 + 5x + 6 x 2 + 6x + 9 c) x 2 + 8x + 15 d) x x Find two integers with the given product and sum. product = 48 and sum = 14 product = 15 and sum = 2 c) product = 30 and sum = 1 d) product = 2 and sum = 3 3. Factor, if possible. x 2 + 8x + 12 c 2 3c 18 c) d d + 21 d) d 2 12d + 35 e) x 2 + x + 1 f) c 2 11c + 30 g) y y + 56 h) x 2 x Determine two values of b so that each expression can be factored. x 2 + bx + 12 x 2 bx + 18 c) x 2 + bx 15 d) x 2 bx Determine two values of c so that each expression can be factored. x 2 + 4x + c x 2 9x + c 7. A parabola has equation y = 3x 2 30x Factor the right side of the equation fully. Identify the x-intercepts of the parabola. c) Find the equation of the axis of symmetry, find the vertex, and draw a graph of the parabola. 8. Determine expressions to represent the dimensions of this rectangular prism. 4. Factor fully by first removing the greatest common factor (GCF). 3x 2 12x 36 2x 2 + 2x + 4 c) 6x 2 42x + 72 d) 3x 2 18x 24 e) 4x 2 40x + 84 f) x 3 + 7x x BLM 5 7 Section 5.4 Practice Master

6 Section 5.5 Practice Master BLM Use algebra tiles or a diagram to factor each trinomial. 2x 2 + 7x + 3 6x x + 4 c) 3x 2 + 7x + 2 d) 4x x Factor. 6x x 4 56x 2 9x 2 c) 9x 2 + 6x + 1 d) 12c 2 26c 16 e) 2d 2 11d 6 f) 2r r + 20 g) 6s 2 29s + 35 h) 15r 2 7r 2 i) 4r 2 20r + 25 j) 13x 2 57x Factor. 6x 2 5xy 4y 2 9x xy + 4y 2 c) 12r 2 + 7rs 10s 2 d) 15r 2 23rs + 4s 2 e) 2x 2 19xy + 42y 2 f) 18y yx 4x 2 4. Find two values of k so that each trinomial can be factored over the integers. 12x 2 + kx x 2 + kx + 10 c) 4x 2 12x + k d) kx 2 40xy + 16y 2 5. The area of a rectangular parking lot is represented by A = 6x 2 19x 7. Factor the expression to find expressions for the length and width. If x represents 15 m, what are the length and width of the parking lot? 6. The height, h, in metres, of a baseball above the ground relative to the horizontal distance, d, in metres, from the batter is given by h = 0.005d d + 1. Write the right side of the equation in factored form. Hint: First divide each term by the common factor, At what horizontal distance from the batter will the baseball hit the ground if it is not caught by an outfielder? 7. Sydney Harbour Bridge in Australia is unusually wide for a long-span bridge. It carries two rail lines, eight road lanes, a cycle lane, and a walkway. Factor the expression 10x 2 7x 3 to find binomials that represent the length and the width of the bridge. If x represents 50 m, what are the length and the width of the bridge, in metres? 8. Factor. 10x 4 3x x 6 59x 3 y y 4 BLM 5 8 Section 5.5 Practice Master

7 Section 5.6 Practice Master BLM Factor. x 2 25 y 2 49 c) 9k 2 1 d) 16k 2 49 e) 25w 2 36 f) 4 9w 2 2. Factor. x 2 y 2 36x 2 y 2 c) 25r 2 36s 2 d) 144r 2 49s 2 e) 121x 2 9y 2 f) 100r 2 81s 2 3. Factor. x x + 49 x 2 6x + 9 c) x 2 8x + 16 d) x + x 2 e) 4x 2 12xy + 9y 2 f) 49x xy + 16y 2 5. Determine the value(s) of b so that each trinomial is a perfect square. bx xy + y 2 36x 2 bxy + 49y 2 6. Determine two values of k so that each trinomial can be factored as a difference of squares. 25x 2 ky 2 kx Factor, if possible. (5c + 3) 2 (2c + 1) (x 3) 2 c) 9x 2 + 8x + 25 d) 25x 2 y 2 150xyab + 225a 2 b 2 8. A parabola has equation y = 4x x Rewrite the equation in factored form to find the coordinates of the vertex. 9. Find an algebraic expression for the area of the shaded region in factored form. 4. Factor fully, if possible. 2a a x 2 16y c) 75x xy + 147y 2 d) 9x 3 y 16xy 3 e) 36m 2 96mn + 64n 2 f) 20x xy + 5y 2 BLM 5 10 Section 5.6 Practice Master

8 Chapter 5 Review BLM (page 1) 5.1 Multiply Polynomials 1. Use the distributive property to find each binomial product. (x + 7)(x + 3) (y 3)(y + 5) c) (x 3y)(x + 2y) d) (3a + 8(5a Expand and simplify. 4(a + 6)(a 3) 3x(x + 2y)(x + 6y) c) (10y + 6)(3y + 7) (y + 2)(y 4) d) 2b(4b 7)(3b + 2) b(5b + 2)(b 6) e) x(x + y)(2x + y) y(3x + y)(x y) 3. A parabola has equation y = 2(x 3)(x 6). Expand and simplify the right side of the equation. State the x-intercepts of the parabola. c) Verify in the expanded form that these are the x-intercepts. 4. Write a simplified algebraic expression to represent the area of the figure. Expand and simplify your expression from part. 5.2 Special Products 5. Draw a diagram to illustrate each product. (x + 5) 2 (y + 3) 2 6. Expand and simplify. (x + 6) 2 (r 3) 2 c) (y + 10) 2 d) (e 5) 2 7. Expand and simplify. (b + 9)(b 9) (y 11)(y + 11) c) (m + 13)(m 13) d) (14 x)(14 + x) 8. Expand and simplify. (x 3y) 2 5(2x c) (11x 13y)(11x + 13y) d) (a 6(a A square has side length 4a. One dimension is increased by 6 and the other is decreased by 6. Write an algebraic expression to represent the area of the resulting rectangle. Expand this expression and simplify. c) Write and simplify an algebraic expression for the change in area from the square to the rectangle. d) Calculate the new area of the rectangle if a represents 5 cm. 5.3 Common Factors 10. Use algebra tiles or a diagram to illustrate the factoring of each polynomial. x 2 + 5x 8x 2 + x 11. Factor. 2x 2 + 4x 5x 2 + 3x c) 10x y 2 d) 3xy 7xz 12. Factor by grouping. 2x 2 + 2x + 3xy + 3y x 3 + x 2 y + yx + y 2 c) 5ab 5a + 3b 3 d) 3a 2 x + 3a 2 y + b 2 x + b 2 y 13. Factor, if possible. 2z(x + y) + 3xy(x + y) x 2 + y 2 + z 2 c) 6a 3 + 3a a + 6 d) x 2 yz 2 x 2 z 2 + xyz BLM 5 11 Chapter 5 Review

9 14. Write an expression in fully factored form for the shaded area. 5.4 Factor Quadratic Expressions of the Form x 2 + bx + c 15. Illustrate the factoring of each trinomial using algebra tiles or a diagram. x 2 + 6x + 9 x x Factor. x 2 4x 12 x 2 7x + 12 c) x 2 4x 45 d) x 2 + 9x Factor completely by first removing the greatest common factor (GCF). 2x x 30 x 3 + 3x 2 28x 18. Determine binomials to represent the length and width of the rectangle, and then determine the dimensions of the rectangle if x = 11 cm. BLM (page 2) 5.5 Factor Quadratic Expressions of the Form ax 2 + bx + c 19. Factor, using algebra tiles or a diagram if necessary. 12x 2 5x 3 3x 2 13x 10 c) 10x 2 + 9x 7 d) 21x 2 + 4x Factor, if possible. 3x y x 2 + 7x + 9 c) 30x 2 + 9x 12 d) 6x 2 34x Find a value of k so that each trinomial can be factored over the integers. 3x 2 + kx 10 24x x + k 5.6 Factor a Perfect Square Trinomial and a Difference of Squares 22. Factor fully. x c 2 25 c) 9x 2 16 d) x 2 e) 1 225y 2 f) 3x y Verify that each trinomial is a perfect square, and then factor. y y + 64 x 2 20x c) y + 9y 2 d) 121c cd + 196d Factor, if possible. 9y y 16 50x 2 60xy + 18y 2 c) (x 3) 2 (y 4) 2 d) x 2 + 9y A rectangular prism has a volume of 4x x 2 + 9x. Determine algebraic expressions for the dimensions of the prism. Describe the faces of the prism. c) Determine the volume if x = 3 cm. d) Determine the surface area if x = 3 cm. BLM 5 11 Chapter 5 Review

10 Chapter 5 Practice Test BLM (page 1) 1. What binomial product does each diagram represent? 4. If it is possible to remove a common factor from the expression 2x 2 + ky + 4, where k is an integer, what can you state about the possible values of k? Explain. 5. Write an algebraic expression for the volume of this rectangular prism. Expand and simplify the expression. c) Find the volume if x = Factor fully. x x r 2 20rs + 4s 2 c) 5x 2 5 d) 1 49m 2 e) 5m m + 6 f) m 2 9mn + 14n 2 2. Expand and simplify. 2x 3 (4x 2 + 2x + 4) xy(6x 2 + xy + 1) 2(x 3 y + 4xy) 3. Expand and simplify. (x 3)(x 9) (2x + 3)(2x 1) c) 3(x 4) 2 + 2(x 3)(x + 3) d) (3c + d) 2 + 2c(c d) e) 2(x 1)(x 6) 3(2x 1) 2 f) (2c + 3d) 2 3(c + 1) 2 7. Factor, if possible. 3y 3 7y 2 + 2y 4m c) 6y 2 + y 1 d) x(m 2) 4(m 2) e) y 2 + 2x + 2y + xy f) 9t 4t 3 8. A ball is thrown into the air and its path is given by h = 5t t + 25, where h is the height, in metres, above the ground and t is the time, in seconds. Factor the right side of the equation fully. When does the ball hit the ground? c) Find the height of the ball 2 s after it is thrown. BLM 5 13 Chapter 5 Practice Test

11 9. Determine two values of k so that each expression can be factored over the integers. x 2 + kx x 2 8x + k c) 36x 2 kxy + 49y 2 d) 49x 2 ky Write and simplify an algebraic expression for the area of the shaded region. 11. The volume of a rectangular prism is represented by the equation V = 12x 3 3x. Factor the right side of the equation fully. Draw a diagram of the prism. c) If x represents 6 cm, what are the dimensions of the prism? BLM (page 2) 13. Describe the steps needed to determine whether the expression ax 3 + bx 2 + cx can be factored over the integers. 14. Factor to evaluate each difference c) d) Two numbers that differ by 2 can be multiplied by squaring their average and then subtracting 1. For example, = , which is 225 1, or 224. How does the product of the sum and difference (x 1)(x + 1) explain the method? Develop a similar method for multiplying two numbers that differ by 4. c) Show how the product of a sum and a difference explains your method from part. 12. The face of a Canadian $20 bill has an area that can be represented by the expression 10x 2 + 9x 40. Factor 10x 2 + 9x 40 to find expressions to represent the dimensions of the bill. If x represents 32 mm, what are the dimensions of the bill, in millimetres? BLM 5 13 Chapter 5 Practice Test

12 Chapter 5 Test BLM (page 1) 1. Represent each binomial product using a diagram. (x + 3)(2x + 1) (2x + 3)(3x + 2) 2. Expand and simplify. 3x 2 y(y 2 x + 4xy 2y 2 ) 4(x 2 + 3x 11) + 5x(x 4) 3. Expand and simplify. (k + 4)(k 1) (6x 1)(x 5) c) 2(3x 2) 2 3(x 1)(x + 5) d) (2x 3y) 2 + 2y(y x) e) 6(1 x)(x + 4) 2(5 2x) 2 4. In baseball, the first base bag is a square. Its side length can be represented by the expression 5x + 3. Write and expand an expression to represent the area of the top of the bag. If x represents 7 cm, what is the area of the top of the bag, in square centimetres? 5. Write an algebraic expression for the volume of the rectangular prism. Expand and simplify the expression. c) Find the volume if x = 1 cm. 6. Factor. x 2 10x x 2 12x + 9 c) 2y 2 + 5y + 2 d) 3k 2 11k 4 e) 10r 2 + r 3 f) 6s 2 11st 10t 2 7. Factor fully, if possible. 21x x 42 7g g 147 c) 3x x 13 d) c 3 9c e) 6d 2 13d + 6 f) 50x A stone is thrown straight down from a tall building. The relation h = 150 5t 5t 2 approximates its path, with h in metres and t in seconds. How tall is the building? Factor the right side of the equation fully. c) When does the stone hit the ground? 9. The North Stone Pyramid at Dahshur in Egypt has a square base with an area that can be represented by the trinomial 9x 2 12x + 4. Factor the trinomial to find a binomial to represent the side length of the base of the pyramid. If x represents 74 m, what is the side length of the base, in metres? BLM 5 14 Chapter 5 Test

13 10. Determine the value(s) of k so that each trinomial can be factored as a perfect square. x 2 12x + k 9x 2 + kx + 25 c) kx 2 4x + 1 d) 16y 2 + ky + 9 e) x 2 + kx + 36 f) 4x 2 24x + k g) 36x 2 kxy + 49y 2 h) 49x 2 42xy + ky 2 BLM (page 2) 13. Explain how to determine the value(s) of k that would make x 2 + kx a perfect square trinomial. 14. If a and b are integers, find values of a and b so that a 2 b 2 is Write an expression for the shaded area in the diagram. 11. Write and simplify an algebraic expression for the area of the shaded region. 12. The area of a rectangle is represented by the equation A = 6x 2 + 5x 4. Factor the right side of the equation fully to find expressions for the length and width of the rectangle. Find an expression for the perimeter of the rectangle. c) If x represents 7 cm, find the area and the perimeter of the rectangle. Factor this expression. c) Find the area of the shaded region if x = 3 cm. BLM 5 14 Chapter 5 Test

14 BLM Answers BLM (page 1) Get Ready 1. monomial trinomial c) trinomial d) binomial e) four-term polynomial c) 3 d) x + 1 8a 5b c) x 2 + 7x 5 d) 6y 3 9y x 2 2xy 5y 2 ab a 2b 2 c) 8x 17 d) 11b 2 b x 2 + 2xy 48a a c) 6a 42 d) 6x 2 + 4x m 2 24m 16x 2 y + 8xy 2 c) 18a 3 24a 3 b d) 2ab a 2 b 14a 7. 30x x 2 62x x 8. 1, 2, 3, 6 1, 2, 17, 34 c) 1, 17 d) 1, 2, 4, 11, 22, c) d) 5 11 c) Section 5.1 Practice Master 1. (x + 1)(x + 3) (x + 2)(x + 2) 2. Diagrams may vary. For example: 3. x 2 + x 6 y 2 + 8y + 12 c) n 2 n 20 d) d d + 42 e) x 2 14x + 48 f) a 2 9a x 2 4y 2 2x 2 5x 3 c) k 2 + k 42 d) 4p 2 24pq + 35q 2 e) 6 13s + 6s 2 f) 6t 2 + rt r x 2 26x 14 x 2 + 7x + 16 c) 29x x 9 d) 8m 2 16m e) 23m 2 26m 9 f) 24x 2 120x x(3x + 1) + 2x(2x + 2 2x) = 6x 2 + 6x (x + 6)(x 3) 2x(x + 1) = x 2 + x x 3 + 9x x c) 6x x + 40 Chapter 5 Practice Masters Answers

15 Section 5.2 Practice Master 1. Diagrams may vary. For example: BLM (page 2) x x 2 y 2 + 9y 4 9x 4 4y 4 c) 6x + 18 d) 13b 2 6b + 6 e) 9x x 3 19x 2 10x + 1 f) 8x 3 36x x 27 Section 5.3 Practice Master 1. Diagrams may vary. For example: 2. x 2 + 8x + 16 y y + 49 c) a a + 64 d) q q y y x xy + 4y 2 c) 4x 2 + 4xy + y 2 d) 36c cd + 49d 2 4. x 2 12x + 36 b 2 50b c) r 2 22r d) e 2 14e a 2 16a + 1 4u 2 12uv + 9v 2 c) 36p 2 84p + 49 d) 25q 2 80qr + 64r 2 6. v 2 4 x 2 36 c) x 2 y 2 d) r 2 s g 2 49h 2 9x 2 y 2 c) g 2 81x 2 d) 16x 2 25y 2 8. V = x 3 + 3x 2 y + 3xy 2 + y 3 SA = 6x xy + 6y 2 9. (3, 0) y = x 2 6x + 9 c) Substitute the coordinates into the left and right sides of the equation. 2 L.S. = x 6x+ 9 R.S. = y 2 = 3 6(3) + 9 = 0 = = 0 L.S. = R.S. 10. the square, by 9 cm 2 c) Chapter 5 Practice Masters Answers

16 2. 3(x + 2y) 17a(c 2d) c) 8xy(2xy 3) d) 9xy(3x 2 y 2 + 2xy + 1) e) 6np 2 (n n 2 p) f) 11c 2 de(3c 2 d 2 e 1) g) 3(g 2 + 2g + 3) 3. (x + 7)(2x + 3) (b 7)(a + 2) c) (r + u)(4s 3) d) (x + s)(y + z) 4. (a + 3)(x + y) 2(x + 2)(2x + 3y) c) (y + 3)(y + d) (5x + 1)(5x + 3y) 5. SA = 2(lw + lh + wh) Both formulas give 340 cm 2 because the formulas are equivalent. 6. (y 6)(3x 2) 2(x 3)(y 2z) 7. 5 (9 2) 2 xy x r2 (π 2) Section 5.4 Practice Master 1. Diagrams may vary. For example: c) d) BLM (page 3) 2. 6, 8 3, 5 c) 6, 5 d) 2, 1 3. (x + 6)(x + 2) (c 6)(c + 3) c) (d + 3)(d + 7) d) (d 5)(d 7) e) not possible f) (c 5)(c 6) g) (y + 7)(y + 8) h) (x 9)(x + 8) 4. 3(x 6)(x + 2) 2(x 2)(x + 1) c) 6(x 4)(x 3) d) 3(x + 2)(x + 4) e) 4(x 7)(x 3) f) x(x + 3)(x + 4) 5. Answers may vary. For example: b = 8, b = 8 b = 9, b = 9 c) b = 2, b = 2 d) b = 3, b = 7 6. Answers may vary. For example: c = 3, c = 5 c = 10, c = (x 8)(x 2) 2, 8 c) x = 5, (5, 27) 8. x by x + 2 by x + 3 Chapter 5 Practice Masters Answers

17 Section 5.5 Practice Master 1. (x + 3)(2x + 1) (2x + 1)(3x + 4) c) (x + 2)(3x + 1) d) 2(x + 2)(2x + 5) 2. 2(x + 2)(3x 1) (7x 2)(8x + 1) c) (3x + 1)(3x + 1) d) 2(2c + 1)(3c 8) e) (d 6)(2d + 1) f) (r + 4)(2r + 5) g) (2s 5)(3s 7) h) (3r 2)(5r + 1) i) (2r 5)(2r 5) j) (x 4)(13x 5) 3. (2x + y)(3x 4y) (3x + 2y)(3x + 2y) c) (3r 2s)(4r + 5s) d) (3r 4s)(5r s) e) (x 6y)(2x 7y) f) (3y + 4x)(6y x) 4. Answers may vary. For example: k = 26, k = 29 k = 16, k = 17 c) k = 5, k = 7 d) k = 9, k = length 3x + 1, width 2x 7 length 46 m, width 23 m (x 100)(x + 2) 100 m 7. 10x + 3, x 1 53 m; 49 m 8. (2x 2 3)(5x 2 + 6) (5x 3 6y 2 )(4x 3 7y 2 ) Section 5.6 Practice Master 1. (x 5)(x + 5) (y 7)(y + 7) c) (3k 1)(3k + 1) d) (4k 7)(4k + 7) e) (5w 6)(5w + 6) f) (2 3w)(2 + 3w) 2. (x y)(x + y) (6x y)(6x + y) c) (5r 6s)(5r + 6s) d) (12r 7s)(12r + 7s) e) (11x 3y)(11x + 3y) f) (10r 9s)(10r + 9s) 3. (x + 7) 2 (x 3) 2 c) (x 4) 2 d) (10 x) 2 e) (2x 3y) 2 f) (7x + 4y) (a + 3) 2 not possible c) 3(5x + 7y) 2 d) xy(3x 4y)(3x + 4y) e) 4(3m 4n) 2 f) 5(2x + y) 2 5. b = 25 b = 84 or b = Answers may vary, but k must be a perfect square. For example: k = 25, k = 4 k = 9, k = (3c + 2)(7c + 4) 2 not possible c) not possible d) 25(xy 3a 2 8. y = 4(x + 4) 2 ; ( 4, 0) 9. A = 4(x + 3)(2x + 1) Chapter 5 Review 1. x x + 21 y 2 + 2y 15 c) x 2 xy 6y 2 d) 15a ab + 48b a 2 12a x 3 24x 2 y 36xy 2 c) 29y y + 50 d) 19b 3 + 2b 2 16b e) 2x 3 6x 2 y + xy 2 + y 3 BLM (page 4) 3. y = 2x 2 18x , 6 c) Substitute the coordinates of the points at the x-intercepts into both sides of the equation. 2 L.S. = y R.S. = 2x 18x+ 36 = 0 2 = 2(6) 18(6) + 36 = = 0 L.S. = R.S. 4. (x 3)(x + 9) 9(x 5) x 2 3x Diagrams may vary. For example: 6. x x + 36 r 2 6r + 9 c) y y d) e 2 10e b 2 81 y c) m d) 196 x 2 8. x 2 6xy + 9y 2 20x 2 100xb 125b 2 c) 121x 2 169y 2 d) 36b 2 a 2 9. (4a + 6)(4a 6) 16a 2 36 c) (4(4 (16a 2 36) = 36 d) 364 cm 2 Chapter 5 Practice Masters Answers

18 10. Diagrams may vary. For example: 11. 2x(x + 2) x(5x + 3) c) 10(x 2 + 2y 2 ) d) x(3y 7z) 12. (x + 1)(2x + 3y) (x + y)(x 2 + y) c) (5a + 3)(b 1) d) (3a 2 + b 2 )(x + y) 13. (x + y)(2z + 3xy) not possible c) 3(2a + 1)(a 2 + 2) d) xz(xyz xz + y) 14. xy(2x + 5) 15. Diagrams may vary. For example: BLM (page 5) 16. (x 6)(x + 2) (x 3)(x 4) c) (x 9)(x + 5) d) (x + 2)(x + 7) 17. 2(x 5)(x 3) x(x + 7)(x 4) 18. length x 9, width x 10; length 2 cm, width 1 cm 19. (3x + 1)(4x 3) (x 5)(3x + 2) c) (2x 1)(5x + 7) d) (3x + 1)(7x 1) 20. 3(x 2 + 5y + 11) not possible c) 3(2x 1)(5x + 4) d) 2(x + 6)(3x 1) 21. Answers may vary. For example: k = 7 k = (x 10)(x + 10) (c 5)(c + 5) c) (3x 4)(3x + 4) d) 2(8 3x)(8 + 3x) e) (1 15y)(1 + 15y) f) 3(x 3y)(x + 3y) 23. Since y 2 = (y) 2 and 64 = 8 2, the first and last terms are perfect squares. Since 16y = 2(y)(8), the middle term is twice the product of the square roots of the first and last terms. Therefore, y y + 64 is a perfect square trinomial. (y + 8) 2 Since x 2 = (x) 2 and 100 = ( 10) 2, the first and last terms are perfect squares. Since 20x = 2(x)( 10), the middle term is twice the product of the square roots of the first and last terms. Therefore, x 2 20x is a perfect square trinomial. (x 10) 2 c) Since 225 = (15) 2 and 9y 2 = ( 3y) 2, the first and last terms are perfect squares. Since 90y = 2(15)( 3y), the middle term is twice the product of the square roots of the first and last terms. Therefore, y + 9y 2 is a perfect square trinomial. (15 3y) 2 This is not fully factored: (15 3y) 2 = [3(5 y)] 2 = 9(5 y) 2 d) Since 121c 2 = (11c) 2 and 196d 2 = (14d) 2, the first and last terms are perfect squares. Since 308cd = 2(11c)(14d), the middle term is twice the product of the square roots of the first and last terms. Therefore, 121c cd + 196d 2 is a perfect square trinomial. (11c + 14d) not possible 2(5x 3y) 2 c) (x + y 7)(x y + 1) d) not possible 25. x by 2x + 3 by 2x + 3 two congruent squares and four congruent rectangles c) 243 cm 3 d) 270 cm 2 Chapter 5 Practice Test 1. (x + 3)(x + 2) (2x + 1)(x + 4) 2. 8x 5 4x 4 8x 3 8x 3 y x 2 y 2 9xy 3. x 2 12x x 2 + 4x 3 c) x x 66 d) 11c 2 + 4cd + d 2 e) 10x 2 2x + 9 f) c cd 6c + 9d k must be divisible by 2, because the only common factor of the other two coefficients is 2. Chapter 5 Practice Masters Answers

19 5. x 2 (3x + 1)(2x + 5) 6x x 3 + 5x 2 c) 252 cubic units 6. (x + 5) 2 (5r 2s) 2 c) 5(x 1)(x + 1) d) (1 7m)(1 + 7m) e) (m + 3)(5m + 2) f) (m 2n)(m 7n) 7. y(y 2)(3y 1) 4(m 2 + 4) c) (2y + 1)(3y 1) d) (m 2)(x 4) e) (x + y)(y + 2) f) t(3 2t)(3 + 2t) 8. 5(t 5)(t + 1) after 5 s c) 45 m 9. Answers may vary. For example: k = 12, k = 13 k = 5, k = 4 c) k = 84, k = 85 d) k = 1, k = 169 (k must be a perfect square) 10. π(r + 3) 2 πr 2 = 3π(2r + 3) 11. 3x(2x 1)(2x + 1) Chapter 5 Test 1. Diagrams may vary. For example: BLM (page 6) c) 18 cm by 11 cm by 13 cm 12. (2x + 5)(5x 8) 69 mm by 152 mm 13. First, remove the greatest common factor, x, to get x(ax 2 + bx + c). Then, find two integers, m and n, whose product is ac and whose sum is b. Break up the middle term, bx, into mx + nx and then factor by grouping = (23 22)( ) = 1(55) = = (25 23)( ) = 2(48) = 96 c) = (81 77)( ) = 4(158) = 632 d) = ( )( ) = 4(204) = You can write any two numbers that differ by 2 as x 1 and x + 1. Their average is x 1+ x+ 1 2x = or x. Their product is 2 2 (x 1)(x + 1), or x 2 1. Find the square of their average and subtract 4. c) Write the two numbers as x 2 and x + 2. Their average is x. Their product is (x 2)(x + 2), or x x 3 y x 3 y 2 6x 2 y 3 x 2 32x k 2 + 3k 4 6x 2 31x + 5 c) 15x 2 36x + 23 d) 4x 2 14xy + 11y 2 e) 14x x (5x + 3) 2 = 25x x cm x(5x 2)(3x + 4) 30x x 2 16x c) 42 cm 3 6. (x 5) 2 (2x 3) 2 c) (y + 2)(2y + 1) d) (k 4)(3k + 1) e) (2r 1)(5r + 3) f) (2s 5t)(3s + 2t) 7. 21(x 1)(x + 2) 7(g 3)(g + 7) c) not possible d) c(c 3)(c + 3) e) (2d 3)(3d 2) f) 2(5x 6)(5x + 6) m 5(t 5)(t + 6) c) after 5 s 9. 3x m Chapter 5 Practice Masters Answers

20 10. k = 36 k = 30, k = 30 c) k = 4 d) k = 24, k = 24 e) k = 12, k = 12 f) k = 36 g) k = 84, k = 84 h) k = (2x + 3)(x + 4) x 2 = x x (2x 1)(3x + 4) 10x + 6 c) 325 cm 2, 76 cm BLM (page 7) 13. Multiply the square root of 100, 10 or 10, by 2, to get 20 or There are eight possible answers for the ordered pair (a, : (5, 2), ( 5, 2), (5, 2), ( 5, 2), (11, 10), ( 11, 10), (11, 10), and ( 11, 10). 15. (2x + 3)(2x + 3) (2)(2) (2x + 1)(2x + 5) c) 77 cm 2 Chapter 5 Practice Masters Answers