Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 1-6 - Cumulative Review: 28

Answer

a) $= 3(x^{2} + 3x - 3)$ b) $= 2(24x^{2} - 74x + 55)$ c) $= 12x^{3} - x^{2} - 43x + 14$

Work Step by Step

$f(x) = 3x^{2} + 5x - 2$ $g(x) = 4x-7$ a) $f(x) + g(x)$ $f(x) + g(x) = 3x^{2} + 5x - 2 + 4x - 7$ $= 3x^{2} + 9x - 9$ $= 3(x^{2} + 3x - 3)$ b) $f(g(x))$ $= f(4x-7)$ $= 3(4x-7)^{2} + 5(4x-7) - 2$ $= 3[(4x)^{2} + 2(4x)(-7) + (-7)^{2}] + 20x - 35 - 2$ $= 3[16x^{2} - 56x + 49] + 20x - 37$ $= 48x^{2} - 168x + 147 + 20x - 37$ $= 48x^{2} - 148x + 147 - 37$ $= 48x^{2} - 148x + 110$ $= 2(24x^{2} - 74x + 55)$ c) $f(x)g(x)$ $= (3x^{2} + 5x - 2)(4x-7)$ $= 4x(3x^{2} + 5x - 2) - 7(3x^{2} + 5x - 2)$ $= 12x^{3}+20x^{2} - 8x - 21x^{2} - 35x + 14$ $= 12x^{3} - x^{2} - 43x + 14$
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