49) If a, b, and c are any integer values except zero, then the terms in the trinomial am3 bm2 cm will always, sometimes, or never have a greatest common factor. always 50) If a, b, and c are any integer values except zero, then the expression ap2 bp c will always, sometimes, or never have a greatest common factor. sometimes Factor completely. 51) 10z2 7z 12 52) 4c2 24c 36 4(c 3)2 53) 9k4 16k2 54) 14m5 63m4 21m3 (5z 4)(2z 3) k2(3k 4)(3k 4) 7m3(2m2 9m 3) 55) d 2 17d 60 56) 4 25 t2 1 9 u2 (d 12)(d 5) a2 57) 3a2b a2 12b 4 58) 8mn 8m 56n 56 8(m 7)(n 1) 59) 25c2 20c 4 (5c 2)2 60) 12v2 32v 5 (6v 1)(2v 5) 61) p2 16 prime 62) x2 9x 12 prime 5 t (7.5) Solve each equation. 63) y(3y 7) 0 64) (2n 3)2 0 65) 2k2 18 13k 66) 3t2 75 0 {5, 5} 67) h2 17h 72 0 68) 21 8p2 2p 69) 121 81r2 70) 12c c2 {12, 0} 71) 3m2 120 18m 72) x(16 x) 63 {7, 9} 73) (w 3)(w 8) 6 {6, 5} 74) 18 9b2 9b {2, 1} 75) (5z 4)(3z2 7z 4) 0 76) 6d 3 45d 33d 2 77) 45p3 20p 0 78) 17v 4(v2 1) (7.6) 79) Find the base and height if the area of the triangle is 18 cm2. x 2 4x 1 80) Find the length and width of the rectangle if its area is 60 in2. x 1 2x 448 CHAPTER 7 Factoring Polynomials 1 3 ub a2 5 t 1 3 ub (3b 1)(a 2)(a 2) e 7 3 , 0 f e 3 2 f e 2, 9 2 f {9, 8} e 3 2 , 7 4 f e 11 9 , 11 9 f {4, 10} e 4 5 , 1, 4 3 f e 0, 5 2 , 3 f e 0, 2 3 , 2 3 f e 1 4 , 4 f base 9 cm; height 4 cm length 12 in.; width 5 in. 81) Find the base and height of the parallelogram if its area is 12 ft2. x x 4 base 6 ft; height 2 ft 82) Find the height and length of the box if its volume is 480 in3. x 5 3x 1 6 in. length 10 in.; width 8 in. 83) Use the Pythagorean theorem to fi nd the length of the missing side. 15 8 17 84) Find the length of the hypotenuse. 13 2x 1 2x x 1 Write an equation, and solve. 85) A rectangular mirror has an area of 10 ft2, and it is 1.5 ft longer than it is wide. Find the dimensions of the mirror. length 4 ft; width 2.5 ft 86) The base of a triangular banner is 1 ft less than its height. If the area is 3 ft2, fi nd the base and height. base 2 ft; height 3 ft 87) The sum of three consecutive integers is one less than the square of the smallest number. Find the integers. 1, 0, 1; or 4, 5, 6 88) The product of two consecutive odd integers is 18 more than the square of the smaller number. Find the integers. 9 and 11 89) Desmond and Marcus leave an intersection with Desmond jogging north and Marcus jogging west. When Marcus is 1 mile farther from the intersection than Desmond, the distance between them is 2 miles more than Desmond’s distance from the intersection. How far is Desmond from the intersection? 3 miles 90) An object is thrown upward with an initial velocity of 68 ft/sec. The height h (in feet) of the object t seconds after it is thrown is given by h 16t 2 68t 60 a) How long does it take for the object to reach a height of 120 ft? 5 4 sec and 3 sec b) What is the initial height of the object? 60 ft c) What is the height of the object after 2 seconds? 132 ft d) How long does it take the object to hit the ground? 5 sec www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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