ANSWERS TO YOU TRY EXERCISES 1) a) (2p 5)(2p 3) b) (5y 4)(2y 1) c) (5a b)(a 6b) 2) a) 3(2h 5)(4h 1) b) 2d(5d 2)(2d 3) 3) a) (2k 1)(k 8) b) (3z 4)(2z 5) 4) a) 2(5y 4)(y 5) b) (4n 3)(n 2) ANSWERS TO TECHNOLOGY EXERCISES 1) (3x 1)(x 4) 2) (2x 5)(x 3) 3) (x 2)(5x 4) 4) (x 1)(2x 3) 5) (x 2)(4x 5) 6) (2x 1)(7x 4) 7.3 Exercises Do the exercises, and check your work. Objective 1: Factor ax2 bx c (a 1) by Grouping 1) Find two integers whose 11) Find the polynomial that factors to (4k 9)(k 2). 12) Find the polynomial that factors to (6m 5)(2m 3). 4k2 17k 18 12m2 28m 15 Complete the factorization. 13) 5t2 13t 6 (5t 3)( ) 14) 4z2 29z 30 (4z 5)( ) 15) 6a2 11a 10 (2a 5)( ) 16) 15c2 23c 4 (3c 4)( ) 17) 12x2 25xy 7y2 (4x 7y)( ) 18) 12r2 52rt 9t2 (6r t) ( ) Factor by grouping. See Example 1. 19) 2h2 13h 15 20) 3z2 13z 14 21) 7y2 11y 4 22) 5a2 21a 18 23) 5b2 9b 18 24) 11m2 18m 8 25) 6p2 p 2 26) 8c2 22c 5 27) 4t2 16t 15 28) 10k2 23k 12 29) 9x2 13xy 4y2 30) 6a2 ab 5b2 Objective 2: Factor ax2 bx c (a 1) by Trial and Error 31) How do we know that (2x 4) cannot be a factor of 2x2 13x 24? 32) How do we know that (3p 2) cannot be a factor of 6p2 25p 14? t 2 z 6 3a 2 5c 1 3x y 2r 9t (2h 3)(h 5) (3z 7)(z 2) (7y 4)(y 1) (5a 6)(a 3) (5b 6)(b 3) (11m 4)(m 2) (3p 2)(2p 1) (4c 1)(2c 5) (2t 3)(2t 5) (5k 4)(2k 3) (9x 4y)(x y) (6a 5b)(a b) because 2 can be factored out of 2x 4, but 2 cannot be factored out of 2x2 13x 24 Since the coeffi cient of the middle term in the trinomial is negative and the constant is positive, both factors will have a minus sign between the terms. *Additional answers can be found in the Answers to Exercises appendix. and whose PRODUCT IS SUM IS ANSWER a) 50 5 b) 27 28 c) 12 8 d) 72 6 a) 10, 5 b) 27, 1 c) 6, 2 d) 12, 6 2) Find two integers whose and whose PRODUCT IS SUM IS ANSWER a) 18 19 b) 132 1 c) 30 13 d) 63 16 a) 18, 1 b) 12, 11 c) 15, 2 d) 9, 7 Factor by grouping. 3) 3c2 12c 8c 32 (3c 8)(c 4) 4) 5y2 15y 2y 6 (5y 2)(y 3) 5) 6k2 6k 7k 7 (6k 7)(k 1) 6) 4r2 4r 9r 9 (4r 9)(r 1) 7) 6x2 27xy 8xy 36y2 (2x 9y)(3x 4y) 8) 14p2 8pq 7pq 4q2 (7p 4q)(2p q) 9) When asked to factor a polynomial, what is the fi rst question you should ask yourself ? Can I factor out a GCF? 10) After factoring a polynomial, what should you ask yourself to be sure that the polynomial is factored completely? Can I factor again? SECTION 7.3 Factoring Trinomials of t www.mhhe.com/messersmith he Form ax2 bx c (a 1) 411
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