Definition/Procedure Example 7.6 Applications of Quadratic Equations Pythagorean Theorem Given a right triangle with legs of length a and b and hypotenuse of length c, c b a the Pythagorean theorem states that a2 b2 c2 (p. 435) Find the length of side a. Let b 4 and c 5 in a2 b2 c2. a2 (4)2 (5)2 a2 16 25 a2 9 0 (a 3)(a 3) 0 b R Reject 3 as a solution since the length of a side cannot be negative. Therefore, a 3. Chapter 7: Review Exercises *Additional answers can be found in the Answers to Exercises appendix. (7.1) Find the greatest common factor of each group of terms. 1) 40, 56 8 2) 36y, 12y2, 54y2 6y 3) 15h 4, 45h 5, 20h3 5h3 4) 4c4d 3, 20c4d 2, 28c2d 4c2d Factor out the greatest common factor. 5) 63t 45 9(7t 5) 6) 21w5 56w 7w(3w4 8) 7) 2p6 20p5 2p4 8) 18a3b3 3a2b3 24ab3 2p4(p2 10p 1) 3ab2(6a2b ab 8b) 9) n(m 8) 5(m 8) 10) x(9y 4) w(9y 4) (m 8)(n 5) (9y 4)(x w) 11) Factor out 5r from 15r3 40r2 5r. 5r(3r2 8r 1) 12) Factor out 1 from z2 9z 4. (z2 9z 4) Factor by grouping. 13) ab 2a 9b 18 14) cd 3c 8d 24 15) 4xy 28y 3x 21 16) hk2 6h k2 6 (a 9)(b 2) (c 8)(d 3) (x 7)(4y 3) (k2 6)(h 1) (7.2) Factor completely. 17) q2 10q 24 18) t2 12t 27 19) z2 6z 72 20) h2 6h 7 21) m2 13mn 30n2 22) a2 11ab 30b2 23) 4v2 24v 64 24) 7c2 7c 84 25) 9w4 9w3 18w2 26) 5x3y 25x2y2 20xy3 (q 6)(q 4) (t 3)(t 9) (z 12)(z 6) (h 7)(h 1) (m 3n)(m 10n) (a 5b)(a 6b) 4(v 8)(v 2) 7(c 4)(c 3) 9w2(w 1)(w 2) 5xy(x 4y)(x y) 5 a 4 a 3 0 or a 3 0 a 3 or a 3 (7.3) Factor completely. 27) 3r2 23r 14 28) 5k2 11k 6 (3r 2)(r 7) 29) 4p2 8p 5 30) 8d 2 29d 12 (2p 5)(2p 1) 31) 12c2 38c 20 32) 21n2 54n 24 33) 10x2 39xy 27y2 (5x 3y)(2x 9y) 34) 6a2 19ab 20b2 (6a 5b)(a 4b) 2(3c 2)(2c 5) 3(7n 4)(n 2) (7.4) Factor completely. 35) w2 49 36) 121 p2 37) 64t2 25u2 38) y4 81 39) 4b2 9 prime 40) 12c2 48d 2 (w 7)(w 7) (11 p)(11 p) (8t 5u)(8t 5u) 41) 64x 4x3 42) 25 9 (y2 9)(y 3)(y 3) h2 a5 3 (5k 6)(k 1) (8d 3)(d 4) 12(c 2d)(c 2d) hba5 3 hb 4x(4 x)(4 x) 43) r2 12r 36 (r 6)2 44) 9z2 24z 16 (3z 4)2 45) 20k2 60k 45 46) 25a2 20ab 4b2 5(2k 3)2 (5a 2b)2 (7.1–7.4) Mixed Exercises For Exercises 47–50, answer always, sometimes, or never. 47) A binomial of the form ax2 bx will always, sometimes, or never factor into a difference of two squares. never 48) A binomial that is the product of two binomials is always, sometimes, or never a difference of two squares. always www.mhhe.com/messersmith CHAPTER 7 Review Exercises 447
messersmith_power_introductory_algebra_1e_ch4_7_10
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