Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - Chapter 5 Review Problem Set: 35

Answer

$x^3-3x^2+8x-12$

Work Step by Step

RECALL: The distributive property states that for any real numbers a, b, and c: $a(b+c) = ab+ac \\a(b-c) = ab - ac$ Use the distributive property (which is shown above) to obtain: $=x(x^2-x+6)-2(x^2-x+6) \\=x(x^2)+x(-x) +x(6)-2(x^2) -2(-x) -2(6) \\=x^3-x^2+6x-2x^2+2x-12$ Combine like terms to obtain: $=x^3 + (-x^2-2x^2)+(6x+2x)-12 \\=x^3+(-3x^2)+8x-12 \\=x^3-3x^2+8x-12$
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