7.2 Exercises Do the exercises, and check your work. Objective 1: Practice Arithmetic Skills Needed for Factoring Trinomials 1) Find two integers whose and whose PRODUCT IS SUM IS ANSWER a) 10 7 b) 56 1 c) 5 4 d) 36 13 a) 5, 2 b) 8, 7 c) 5, 1 d) 9, 4 2) Find two integers whose and whose PRODUCT IS SUM IS ANSWER a) 42 13 b) 14 13 c) 54 15 d) 21 4 a) 7, 6 b) 14, 1 c) 6, 9 d) 7, 3 Objective 2: Factor a Trinomial of the Form x2 bx c 3) If x2 bx c factors to (x m)(x n) and if c is positive and b is negative, what do you know about the signs of m and n? They are negative. 4) If x2 bx c factors to (x m)(x n) and if b and c are positive, what do you know about the signs of m and n? They are positive. 5) When asked to factor a polynomial, what is the fi rst question you should ask yourself ? Can I factor out a GCF? 6) What does it mean to say that a polynomial is prime? It does not factor. 7) After factoring a polynomial, what should you ask yourself to be sure that the polynomial is completely factored? Can I factor again? 8) How do you check the factorization of a polynomial? Multiply the factors. The product should be the original polynomial. Complete the factorization. 9) n2 7n 10 (n 5)( n 2 ) 10) p2 11p 28 ( p 4)( p 7 ) 11) c2 16c 60 (c 6)(c 10 ) 12) t2 12t 27 (t 9)( t 3 ) 13) x2 x 12 (x 3)( x 4 ) 14) r2 8r 9 (r 1)( r 9 ) Factor completely, if possible. Check your answer. 15) g2 8g 12 16) p2 9p 14 17) y2 10y 16 18) a2 11a 30 19) w2 17w 72 20) d2 14d 33 21) b2 3b 4 22) t2 2t 48 23) z2 6z 11 prime 24) x2 7x 15 prime 25) c2 13c 36 26) h2 13h 12 27) m2 4m 60 28) v2 4v 45 29) r2 4r 96 30) a2 21a 110 31) q2 12q 42 prime 32) d 2 15d 32 prime 33) x2 16x 64 34) c2 10c 25 35) n2 2n 1 36) w2 20w 100 37) 24 14d d2 38) 10 7k k2 39) 56 12a a2 prime 40) 63 21w w2 prime (g 6)(g 2) (p 7)(p 2) (y 8)(y 2) (a 6)(a 5) (w 9)(w 8) (d 3)(d 11) (b 4)(b 1) (t 6)(t 8) (c 9)(c 4) (h 1)(h 12) (m 10)(m 6) (v 9)(v 5) (r 12)(r 8) (a 11)(a 10) (x 8)(x 8) or (x 8)2 (c 5)(c 5) or (c 5)2 (n 1)(n 1) or (n 1)2 (w 10)(w 10) or (w 10)2 (d 12)(d 2) (k 5)(k 2) Objective 3: More on Factoring a Trinomial of the Form x2 bx c Factor completely, if possible. Check your answer. 41) 2k2 22k 48 42) 6v2 54v 120 43) 50h 35h2 5h3 44) 3d 3 33d 2 36d 45) r4 r3 132r2 46) 2n4 40n3 200n2 47) 7q3 49q2 42q 48) 8b4 24b3 16b2 49) 3z4 24z3 48z2 50) 36w 6w2 2w3 51) xy3 2xy2 63xy 52) 2c3d 14c2d 24cd 2(k 3)(k 8) 6(v 4)(v 5) 5h(h 5)(h 2) 3d(d 12)(d 1) r2(r 12)(r 11) 2n2(n 10)(n 10) or 2n2(n 10)2 7q(q2 7q 6) 8b2(b 2)(b 1) 3z2(z 4)(z 4) or 3z2(z 4)2 2w(w 3)(w 6) xy(y 9)(y 7) 2cd(c2 7c 12) Factor completely by fi rst taking out 1 and then factoring the trinomial, if possible. Check your answer. 53) m2 12m 35 54) x2 15x 36 (m 5)(m 7) (x 12)(x 3) 55) c2 3c 28 56) t2 2t 48 (c 7)(c 4) (t 8)(t 6) 57) z2 13z 30 58) n2 16n 55 (z 3)(z 10) (n 11)(n 5) 59) p2 p 56 60) w2 2w 3 (p 8)(p 7) (w 1)(w 3) Objective 4: Factor a Trinomial Containing Two Variables Factor completely. Check your answer. 61) x2 7xy 12y2 62) a2 11ab 18b2 63) c2 7cd 8d2 64) p2 6pq 72q2 (x 4y)(x 3y) (a 9b)(a 2b) (c 8d)(c d) (p 12q)(q 6q) *Additional answers can be found in the Answers to Exercises appendix. 404 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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