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83) 7cd 12 28c 3d 84) 9rs 12 2s 54r 85) 42k  3 15d 2 18k  2d 35kd 86) 12x3 2y2 3x2y 8xy 87) 9f 2j2 45f j 9f j2 45f 2j 88) n3m 4n2 mn2 4n3 89) 4x4y 14x3 28x4 2x3y 90) 12a2c2 20ac 4ac2 60a2c Mixed Exercises: Objectives 1–5 Factor completely. 91) pq 8p 3q 24 92) 27d 3 36d 2 9d 93) a4b2 2a3b3 8a2b4 94) 18rt3 15t3 18rt2 15t2 95) 3h3 8k3 12h2k2 2hk 96) 6yz 8z 3y 4 97) 2c4 14c2 84c 12c3 98) 18w3 45w2 99) Factor out 8v from 16v3 56v2 8v. 100) Factor out 3n2 from 3n4 27n3 33n2. Factor completely. You may need to begin by taking out the GCF fi rst or by rearranging terms. Fill It In Fill in the blanks with either the missing mathematical step or reason for the given step. 77) 5mn 15m 10n 30 5mn 15m 10n 30 Factor out the GCF. 5m(n 3) 2(n 3) Take out the binomial 78) 3x2y 21x2 6xy 42x 3x2y 21x2 6xy 42x Factor out the GCF. 3xx(y 7) 2(y 7) Take out the 79) 7pq 28q 14p 56 80) 2ab 8a 6b 24 81) 8s2t 40st 16s2 80s 82) 10hk3 5hk  factor. 2 30k3 15k  binomial factor. 2 R1) Why is the GCF for x4 x3 x2 not equal to x4, the term with the largest exponent power? R2) Why are x and (x 4) considered to be factors of x2 4x? R3) How does multiplying two binomials together relate to factoring a trinomial? R4) Can the factoring by grouping procedure be performed on a trinomial? Why or why not? R5) Which exercises in this section do you fi nd most challenging? www.mhhe.com/messersmith SECTION 7.1 The Greatest Common Factor and Factoring by Grouping 365


messersmith_power_intermediate_algebra_1e_ch4_7_10
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