MATH 830/GRACEY EXAM 5 PRACTICE/CH MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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1 MATH 830/GRACEY EXAM 5 PRACTICE/CH Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the greatest common factor of the monomials. 1) 6x2 and 18 A) 6x2 B) 6 C)6x D) 3 1) 2) 8x6 and 12x3 A) 8x3 B) 4x3 C) 4x6 D) 12x3 2) 3) 21y3 and 189y7 A) 21y3 B) 21y4 C) 189y3 D) 3969y4 3) 4) 12xy, -18x2, -18xy2, and -14y2 A) 2x B) 2 C)4 D) 2xy 4) Factor out the GCF from the polynomial. 5) 4x - 24 A) -96x B) 4(x - 24) C)4(x - 6) D) 4x - 6 5) 6) 5x4 + 40x2 A) 5x3(x + 8x) B) 5(x4 + 8x2) C)x4(5x2 + 40) D) 5x2(x2 + 8) 6) 7) 6x3 + 1 A) 6(x3 + 6) B) 6(x3 + 1) 7) C)6 x D) No common factor 8) 14x2-11x4 A) 14(x2-154) B) x2(14-11x2) C)x2(1-11x2) D) 14x x 2 8) 9) 32m7-16m5 + 24m2 A) 8m2(4m5-2m3 + 3) B) 8(4m7-2m5 + 3m2) C)No common factor D) m2(32m5-16m3 + 24) 9) 10) 120x6y9-36x4y6-60x2y4 A) 12x2y4(10x4y5-3x2y2-5) B) No common factor C)12x2(10x4y9-3x2y6-5y4) D) 12(10x6y9-3x4y6-5x2y4) 10) 11) 72x8y8-96x5y6-120x2y2 A) -24x2y2(-3x6y6-4x3y4 + 5) B) 24x2(3x6y8-4x3y6-5y2) C)24(3x8y8-4x5y6-5x2y2) D) 24x2y2(3x6y6-4x3y4-5) 11) 1
2 Write a polynomial for the width of the rectangle. 12) Write a polynomial for the width of the rectangle. 5x3 12)? Area = 5x4 + 15x3 square units A) 5x4 + 10x3 B) x4 + 3x3 C)x + 3 D) x + 15x3 Factor the polynomial using the greatest common binomial factor. 13) x(x + 14) + 8(x + 14) A) (x2 + 14)(x2 + 8) B) (x - 14)(x - 8) C)(x2 + 14x)(8x + 112) D) (x + 14)(x + 8) 13) 14) x(x - 12) + 8(x - 12) A) (x - 12)(x - 8) B) (x2-12x)(8x - 96) C)(x + 12)(x - 8) D) (x - 12)(x + 8) 14) 15) xy(x - 2) + (x - 2) A) (x - 2)(xy + 1) B) (x - 2)(xy - 1) C)xy(x - 2) D) (x2y - 2xy) + (x - 2) 15) Factor by grouping. 16) x4 - x3 + 6x - 6 A) (x3 + 6)(6x - 1) B) (x3-6)(x - 1) C)(x3 + 6)(x - 1) D) (x3-1)(x + 6) 16) 17) 6x6-15x3 + 10x3-25 A) (3x3-5)(2x3 + 5) B) (3x3 + 5)(2x3-5) C)(6x3-5)(x3 + 5) D) (3x6 + 5)(2x - 5) 17) 18) 6x3-9x2y + 10xy2-15y3 A) (3x2 + 5y)(2x - 3y) B) (3x2 + 5y2)(2x - 3y) C)(6x2 + 5y2)(x - 3y) D) (3x2-5y2)(2x + 3y) 18) 2
3 Write a polynomial for the length of the rectangle. 19)? 19) x - 7 Area = x2-5x - 7x + 35 square units A) x + 35 B) x - 5 C)x2 + 7 D) x2-6x - 7x + 30 Factor completely. 20) x2 - x - 20 A) (x + 5)(x - 4) B) (x + 1)(x - 20) C)(x + 4)(x - 5) 20) 21) x2 + 2x - 15 A) (x- 5)(x + 1) B) (x + 5)(x - 3) C)(x - 5)(x + 3) 21) 22) x2 + 11x + 30 A) (x- 5)(x + 6) B) (x + 5)(x + 6) C)(x - 5)(x + 1) 22) 23) x2 + 13xy + 40y2 A) (x- 5y)(x + 8y) B) (x- 5y)(x + y) C)(x + 5y)(x + 8y) 23) 24) u2-4uv - 45v2 A) (u- 5v)(u + 9v) B) (u + 5v)(u - 9v) C)(u - 5v)(u + v) 24) 25) x2 + 5xy - 104y2 A) (x + 13y)(x - 8y) B) (x- 13y)(x + y) C)(x - 13y)(x + 8y) 25) 26) x3 - x2-6x A) (x2 + 1)(x - 6) B) x(x + 3)(x - 2) C)x(x + 2)(x - 3) 26) 27) 3x6-12x5-63x4 A) x4(3x + 9)(x - 7) B) 3x4(x + 3)(x - 7) C)3x4(x2-4x - 21) D) x4(x + 3)(3x - 21) 27) 3
4 28) 2x2-6xy - 8y2 A) (2x - 2y)(x + 4y) B) 2(x + y)(x - 4y) C)2(x - y)(x + 4y) D) prime 28) 29) x3y - 3x2y2-28xy3 A) y(x - 7y)(xy + 4y2) B) xy(x2-3x - 28y2) C)xy(x - 7y)(x + 4y) D) x(xy - 7y2)(x + 4y) 29) 30) x2(y - 7) - 14x(y - 7) + 45(y - 7) A) (x- 9)(x - 5)(y - 7) B) (x- 9)(x + 5)(y - 7) C)(x + 9)(x - 5)(y - 7) D) (x + 9)(x + 5)(y - 7) 30) Factor completely. If unfactorable, indicate that the polynomial is prime. 31) (a + b)x2-5(a + b)x - 36(a + b) A) (a + b)(x + 4)(x - 9) B) (ax + 4b)(ax - 9b) C)(a +b)(x - 4)(x + 9) 31) 32) x2-2 9 x ) A) x x B) x x C) x x ) -x2 + 5x + 24 A) (x- 3)(x + 8) B) -(x + 3)(x - 8) C) -(x- 3)(x + 8) 33) Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. 34) 3x2 + 34x + 11 A) prime B) (3x + 1)(x + 11) C)(3x - 1)(x - 11) D) (3x + 11)(x + 1) 34) 35) 2x2-11x + 15 A) prime B) (2x - 5)(x - 3) C)(2x + 3)(x + 5) D) (2x - 3)(x - 5) 35) 36) 8y2 + 18y + 9 A) (2y + 3)(4y + 3) B) (2y- 3)(4y - 3) C)prime D) (8y + 3)(y + 3) 36) 37) 15x2-4x - 3 A) (x + 1)(15x - 3) B) (3x - 1)(5x + 3) C)(3x + 1)(5x - 3) D) (5x + 1)(3x - 3) 37) 38) 12x2-5xt - 2t2 A) (4x - t)(3x + 2t) B) (4x + t)(3x - 2t) C)(12x + t)(x - 2t) D) prime 38) 39) -36x2-30x + 36 A) -6(3x + 2)(2x - 3) B) -6(3x - 2)(2x + 3) C)prime D) (-18x + 12)(2x + 3) 39) 4
5 40) 8x2y2-10xy2-25y2 A) y2(4x + 5)(2x - 5) B) y2(x + 5)(8x - 5) C)(2x + 5y)(4x - 5y) D) (4x + 5y)(2x - 5y) 40) 41) 25x3y4 + 40x2y5 + 16xy6 A) y4(5x + 4y)(5x2 + 4xy) B) xy4(5x + 4y)(5x + 4y) C)x(5xy4 + 4y5)(5x + 4y) D) prime 41) Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. 42) 2x2 + 23x + 11 A) (2x - 1)(x - 11) B) prime C)(2x + 11)(x + 1) D) (2x + 1)(x + 11) 42) 43) 3x2 + 13x + 10 A) (3x + 5)(x + 2) B) (3x + 2)(x + 5) C)(3x - 5)(x - 2) D) prime 43) 44) 12z2-7z - 12 A) (4z + 3)(3z - 4) B) prime C)(12z + 3)(z - 4) D) (4z - 3)(3z + 4) 44) 45) 6x2-7xt - 3t2 A) (6x + t)(x - 3t) B) (3x + t)(2x - 3t) C)(3x - t)(2x + 3t) D) prime 45) 46) 108x2 + 63xy + 9y2 A) 9(3x + y)(4x + y) B) (27x + 9y)(4x + y) C)9(3x - y)(4x - y) D) prime 46) 47) 15x2y2 + 34xy2 + 15y2 A) y2(3x + 5)(5x + 3) B) (3x + 5y)(5x + 3y) C)y2(x + 5)(15x + 3) D) (5x + 5y)(3x + 3y) 47) 48) x4-9x3 + 14x2 A) x2(x - 7)(x + 2) B) x2(x - 7)(x - 2) C)x-7(x2-9x + 14) D) x2(x + 7)(x - 2) 48) 49) 15x3y4 + 32x2y5 + 16xy6 A) xy4(5x + 4y)(3x + 4y) B) prime C)x(5xy4 + 4y5)(3x + 4y) D) y4(5x + 4y)(3x2 + 4xy) 49) 5
6 Solve the problem. 50) The length and area of the rectangle are given. Express the width as a binomial. 50) 6x + 4? Area of rectangle = 12x2-22x - 20 A) 2x + 4 B) 6x + 5 C)2x - 5 D) Not enough information. Factor completely. If unfactorable, indicate that the polynomial is prime. 51) 81x2-64 A) (9x + 8)(9x - 8) B) (9x + 8)2 C)(9x - 8)2 51) 52) 25k2-81m2 A) (5k- 9m)2 B) (5k + 9m)2 C)(5k + 9m)(5k - 9m) 52) 53) z2-4 A) (z - 2)2 B) (z + 2)(z - 2) C)(z + 2)2 53) 54) s6 - t6 A) (s4 - t4) 2 B) (s4 + t4)(s4 - t4) C)(s3 + t3)(s3 - t3) D) (s3 - t3) 2 54) 55) 121t12-1 A) (11t6 + 1 ) 2 B) (11t6-1 ) 2 C)(11t6 + 1)(11t6-1 ) 55) 56) 3x2-192 A) 3(x + 8)2 B) 3(x + 8)(x - 8) C)3(x - 8)2 56) 57) 17x2-17 A) 17(x + 1)2 B) 17(x + 1)(x - 1) C)17(x - 1)2 57) 58) 36 - (x + 2y)2 A) (6 + x - 2y)(6 - x - 2y) B) (6 + x + y)(6 - x - y) C)(6 + x + 2y)(6 - x - 2y) D) (6 + 2xy)(6-2xy) 58) 6
7 59) 64x ) A) 8x x B) 64x x C) 8x D) 8x Solve the problem. 60) Express the shaded area as the product of two binomials. 8x 60) 8x t t A) 8(8 - t) B) (8x - t)(8x - t) C)(8x + t)(8x - t) D) (x + 8t)(x - 8t) Factor completely. If unfactorable, indicate that the polynomial is prime. 61) x2 + 12x + 36 A) (x + 6)(x - 6) B) (x - 6)2 C)(x + 6)2 61) 62) x2-15x A) (x + 15)2 B) (x + 15)(x - 15) C)(x - 15)2 62) 63) z2 + 14z + 49 A) (z - 7)2 B) (z + 7)2 C)(z + 7)(z - 7) D) (z + 14)(z - 14) 63) 64) 81k3m + 72k2m2 + 16km3 A) (81mk2 + km)(k + 16m2) B) km(9k + 4m)(9k - 4m) C)km(9k - 4m)2 D) km(9k + 4m)2 64) 65) 125x2y + 200xy2 + 80y3 A) 5y(5x + 4y)2 B) 5(5x + 4y)2 C)5y(5x - 4y)2 D) 5y(x + 4y)(x - 4y) 65) 7
8 Factor completely. 66) 216p3-1 A) (216p- 1)(p2 + 6p + 1) B) (6p + 1)(36p2-6p + 1) C)(6p - 1)(36p2 + 1) D) (6p - 1)(36p2 + 6p + 1) 66) 67) x3-512 A) (x - 8)(x2 + 8x + 64) B) (x - 8)(x2 + 64) C)(x + 512)(x2-1) D) (x + 8)(x2-8x + 64) 67) 68) t A) (t + 7)(t2 + 49) B) (t - 343)(t2-1) C)(t + 7)(t2-7t + 49) D) (t - 7)(t2 + 7t + 49) 68) 69) a3b A) (ab - 3)(a2b2 + 3ab + 9) B) (ab - 3)(a2b2 + 9) C)(ab + 3)(a2b2-3ab + 9) D) (ab + 3)(a2b2-9) 69) 70) 64 - t3 A) (4 - t)(16 + t2) B) (4 - t)(16 + 4t + t2) C)(4 + t)(16 - t2) D) (4 + t)(16-4t + t2) 70) 71) x4 - x ) A) x x x x B) x x2-1 6 x x C) x2-1 6 x x D) x x x2-1 6 x Factor. 72) 63m9 + 45m7 + 90m4 A) -m4(-63m5 + 45m3-90) B) m4(63m5 + 45m3 + 90) C)9(7m9 + 5m7 + 10m4) D) 9m4(7m5 + 5m3 + 10) 73) xy + y + 4x + 4 A) (x + 4)(y + 1) B) (4x + 4)(y + 1) C)(x + 1)(4y + 4) D) (x + 1)(y + 4) 72) 73) 74) 5x2 + 19x - 4 A) (5x - 1)(x + 4) B) (5x - 4)(x + 1) C)(5x + 1)(x - 4) D) (5x + 4)(x - 1) 74) 75) z2 + 10z + 25 A) (z + 5)2 B) (z + 5)(z - 5) C)(z + 10)(z - 10) D) (z - 5)2 75) 76) 49x2-64 A) (7x - 8)2 B) (7x + 8)2 C)(7x + 8)(7x - 8) D) prime 76) 8
9 77) t A) (t + 9)(t2 + 81) B) (t - 9)(t2 + 9t + 81) C)(t + 9)(t2-9t + 81) D) (t - 729)(t + 1)(t - 1) 77) 78) x3-64 A) (x + 64)(x + 1)(x - 1) B) (x - 4)(x2 + 16) C)(x - 4)(x2 + 4x + 16) D) (x + 4)(x2-4x + 16) 78) Factor completely. If unfactorable, indicate that the polynomial is prime. 79) 9x7-9x5 A) 9x5(x - 1)2 B) 9x5(x + 1)(x - 1) C)9x5(x + 1)2 79) 80) 2x4-16x3 + 32x2 A) x4(2x - 8)(x - 4) B) 2x4(x2-8x + 16) C)2x2(x - 4)2 D) 2x4(x + 4)2 80) 81) 49x10 + y10 A) (7x5 - y5) 2 B) (7x5 + y5) 2 C)(7x5 + y5)(7x5 - y5) 81) 82) 80m9-56m7-80m4 A) 8m4(10m5-7m3-10) B) m4(80m5-56m3-80) C)8(10m9-7m7-10m4) 82) 83) 81k3m - 90k2m2 + 25km3 A) km(9k + 5m)2 B) km(9k - 5m)2 C)km(9k - 5m)(9k + 5m) 83) 84) x2 + 17x + 18 A) (x- 9)(x + 2) B) (x + 9)(x - 2) C)(x + 18)(x - 1) 84) 85) x4-8x2-9 A) (x2-9)(x2 + 1) B) (x + 3)(x - 3)(x + 1)(x - 1) C)(x + 3)(x - 3)(x2 + 1) D) (x - 3)2(x2 + 1) 85) 86) x4 + 2x x A) (x + 2)(x + 5)(x2-5x + 25) B) (x + 2)(x - 5)(x2 + 5x + 25) C)(x + 2)(x ) D) prime 86) 87) x16 + 8x A) x(x5 + 2)(x10-2x5 + 4) B) (x5 + 4)(x10 - x5 + 2) C)x(x10 + 1)(x10-2x5 + 8) D) x(x5-2)(x10 + 2x5 + 4) 87) 9
10 Solve the problem. 88) The model of a building has the shape of a rectangular solid. The height is represented by x inches. The base of the model is square and the volume of the model is x3-120x x. Express the area of the model's base in terms of x. 88) x inches A) 120x square inches B) x square inches C)(x + 60)(x - 60) square inches D) (x - 60)2 square inches 89) A circle of radius r is inscribed in a square with sides 2r as shown in the figure. Express the total of the shaded areas in terms of r and π as a completely factored polynomial. 89) A) r2(2 + π)(2 - π) B) r2(4 - π) C)r(2-π)2 D) π2(4 - r) Solve the equation. 90) (x- 5)(x + 4) = 0 A) {-5, 4} B) {-4, 5} C){5, 4} D) {-5, 5, -4, 4} 90) 91) (9x + 23)(3x + 22) = 0 A) {14, 19} B) 23 9, 22 3 C) , D) , ) 92) x(x + 11) = 0 A) {0, 11} B) {-11,-1} C){-11, 0} D) {-11, 1} 92) 93) x2 - x = 42 A) {-6, 7} B) {1, 42} C){6, 7} D) {-7,-6} 93) 10
11 94) 3x2-27x + 60 = 0 A) {0, 4, 5} B) {4, 3, 5} C){4, 5} D) {-5,-4} 94) 95) 36x2 = 25 5 A) 36 B) 5 6 C) , 5 36 D) - 5 6, ) 96) 16x2-5x = 0 A) 0, 5 16 B) , 0 C) , 0 D) 0, ) 97) x2-64 = 63x A) {-8} B) {-1, 64} C){-8, 8} D) {-64, 1} 97) 98) x2 = -16x - 64 A) {-8} B) {0, 8} C){8} D) {-8, 8} 98) Solve the problem. 99) The perimeter of the quadrilateral is 88 inches. Find the lengths of the sides. 99) A) 10 in., 20 in., 54 in., 4 in. B) 12 in., 21 in., 70 in., 5 in. C)11 in., 19 in., 54 in., 4 in. D) 3 in., 3 in., -2 in., -4 in. 100) If the sides of a square are increased by 2 meters, the area becomes 49 square meters. Find the length of a side of the original square. A) 2 m B) 9 m C)7 m D) 5 m 100) 101) A window washer accidentally drops a bucket from the top of a 256-foot building. The height h of the bucket after t seconds is given by h = -16t When will the bucket hit the ground? A) 64 sec B) 4 sec C) -4 sec D) 16 sec 101) 102) The equation D = 1 n(n - 3) gives the number of diagonals D for a polygon with n sides. Use this 2 102) equation to solve the problem. Find the number of sides n for a polygon that has 20 diagonals. A) 5 sides B) 3 sides C)8 sides D) 9 sides 103) A triangular piece of glass is being cut so that the height of the triangle is 4 inches shorter than twice the base. If the area of the triangle is 224 square inches, how long is the height of the triangle? A) 30 in. B) 28 in. C)32 in. D) 16 in. 103) 11
12 Answer Key Testname: M830E5PRAC 1) B 2) B 3) A 4) B 5) C 6) D 7) D 8) B 9) A 10) A 11) D 12) C 13) D 14) D 15) A 16) C 17) B 18) B 19) B 20) C 21) B 22) B 23) C 24) B 25) A 26) C 27) B 28) B 29) C 30) A 31) A 32) B 33) B 34) B 35) A 36) A 37) C 38) B 39) B 40) A 41) B 42) D 43) D 44) A 45) B 46) A 47) A 48) B 49) A 50) C 12
13 Answer Key Testname: M830E5PRAC 51) A 52) C 53) B 54) C 55) C 56) B 57) B 58) C 59) A 60) C 61) C 62) D 63) B 64) D 65) A 66) D 67) A 68) C 69) C 70) B 71) A 72) D 73) D 74) A 75) A 76) C 77) C 78) C 79) B 80) C 81) D 82) A 83) B 84) D 85) C 86) A 87) A 88) D 89) B 90) B 91) C 92) C 93) A 94) C 95) D 96) A 97) B 98) A 99) C 100) D 13
14 Answer Key Testname: M830E5PRAC 101) B 102) C 103) B 14
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