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7-6 Mulitplying a Polynomial by a Monomial Find each product. 2 3 7 3 2 3 6. c d (5cd − 3c d − 4d ) SOLUTION: Simplify each expression. 2 8. x(3x + 4) + 2(7x − 3) SOLUTION: 2 2 2 4 2 10. −5w (8w x − 11wx ) + 6x(9wx − 4w − 3x ) SOLUTION: Solve each equation. 12. −6(11 − 2c) = 7(−2 − 2c) SOLUTION: eSolutions Manual - Powered by Cognero Page 1 7-6 Mulitplying a Polynomial by a Monomial Solve each equation. 12. −6(11 − 2c) = 7(−2 − 2c) SOLUTION: 14. −2(w + 1) + w = 7 − 4w SOLUTION: 16. a(a + 3) + a(a − 6) + 35 = a(a − 5) + a(a + 7) SOLUTION: Find each product. 2 18. b(b − 12b + 1) eSolutions Manual - Powered by Cognero SOLUTION: Page 2 7-6 Mulitplying a Polynomial by a Monomial Find each product. 2 18. b(b − 12b + 1) SOLUTION: 3 3 2 20. −3m (2m − 12m + 2m + 25) SOLUTION: 2 2 22. 2pr (2pr + 5p r − 15p ) SOLUTION: Simplify each expression. 2 24. −3(5x + 2x + 9) + x(2x − 3) SOLUTION: 2 26. −4d(5d − 12) + 7(d + 5) eSolutions Manual - Powered by Cognero SOLUTION: Page 3 7-6 Mulitplying a Polynomial by a Monomial 2 26. −4d(5d − 12) + 7(d + 5) SOLUTION: 2 2 2 2 2 2 28. 2j (7j k + j k + 5k) − 9k(−2j k + 2k + 3j ) SOLUTION: 30. DAMS A new dam being built has the shape of a trapezoid. The base at the bottom of the dam is 2 times the height. The base at the top of the dam is times the height minus 30 feet. a. Write an expression to find the area of the trapezoidal cross section of the dam. b. If the height of the dam is 180 feet, find the area of this cross section. SOLUTION: a. The equation for the area of a trapezoid is Manual - Powered by Cognero eSolutions b 1 = 2h . Page 4 7-6 Mulitplying a Polynomial by a Monomial 30. DAMS A new dam being built has the shape of a trapezoid. The base at the bottom of the dam is 2 times the height. The base at the top of the dam is times the height minus 30 feet. a. Write an expression to find the area of the trapezoidal cross section of the dam. b. If the height of the dam is 180 feet, find the area of this cross section. SOLUTION: a. The equation for the area of a trapezoid is . b 1 = 2h b2 = b. Let h = 180. So, the area is 32,940 square feet. Simplify each expression. 2 2 3 2 3 2 3 2 40. −x z(2z + 4xz ) + xz (xz + 5x z) + x z (3x z + 4xz) eSolutions Manual - Powered by Cognero SOLUTION: Page 5 7-6 Mulitplying a Polynomial by a Monomial So, the area is 32,940 square feet. Simplify each expression. 2 2 3 2 3 2 3 2 40. −x z(2z + 4xz ) + xz (xz + 5x z) + x z (3x z + 4xz) SOLUTION: 42. PETS Che is building a dog house for his new puppy. The upper face of the dog house is a trapezoid. If the height of the trapezoid is 12 inches, find the area of the face of this piece of the dog house. SOLUTION: The formula for the area of a trapezoid is . Now substitute h = 12 inches into the equation. eSolutions Manual - Powered by Cognero Page 6 7-6 Mulitplying a Polynomial by a Monomial 42. PETS Che is building a dog house for his new puppy. The upper face of the dog house is a trapezoid. If the height of the trapezoid is 12 inches, find the area of the face of this piece of the dog house. SOLUTION: The formula for the area of a trapezoid is . Now substitute h = 12 inches into the equation. Therefore, the area of the trapezoid is 318 square inches. 52. If a = 5x + 7y and b = 2y − 3x, what is a + b? F 2x − 9y G 3y + 4x H 2x + 9y J 2x − 5y SOLUTION: So, the correct choice is H. 54. SHORT RESPONSE Write an equation in which x varies directly as the cube of y and inversely as the square of z. SOLUTION: If x varies directly as the cube of y, then both x and y must be in the numerators on either side of the equal sign. When x varies inversely with the square of z. then the z must be in the denominator. Then . The eSolutions Manual - Powered by Cognero combination of the two is Page 7 . 7-6 Mulitplying a Polynomial by a Monomial So, the correct choice is H. 54. SHORT RESPONSE Write an equation in which x varies directly as the cube of y and inversely as the square of z. SOLUTION: If x varies directly as the cube of y, then both x and y must be in the numerators on either side of the equal sign. When x varies inversely with the square of z. then the z must be in the denominator. Then . The combination of the two is . Find each sum or difference. 2 2 56. (3z + 2z − 1) + (z − 6) SOLUTION: 3 2 3 60. (8c − 3c + c − 2) − (3c + 9) SOLUTION: Find the degree of each polynomial. 62. −10 SOLUTION: A constant has a degree of 0. 3 64. 9a − 8a + 6 SOLUTION: The degree of a polynomial is the greatest degree of any term in the polynomial. Find the degree of each term: 9a: degree 1 3 −8a : degree 3 6: degree 0 The degree of the polynomial is 3. 4 52 66. −3p r t SOLUTION: To find the degree of monomial, add the degrees of each variable: 4 + 5 + 2 = 11. Write an equation in function notation for each relation. eSolutions Manual - Powered by Cognero Page 8 4 52 66. −3p r t SOLUTION: 7-6 Mulitplying a Polynomial by a Monomial To find the degree of monomial, add the degrees of each variable: 4 + 5 + 2 = 11. Write an equation in function notation for each relation. 68. SOLUTION: The y-intercept is 0. Find the slope by choosing two points. Choose (0, 0) and (1, 4). So the slope intercept form is f (x) = 4x + 0 or f (x) = 4x. eSolutions Manual - Powered by Cognero Page 9

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