Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.5 Apply the Remainder and Factor Theorems - 5.5 Exercises - Mixed Review - Page 368: 59

Answer

$9x^4-6x^3-8x^2-24x+32$

Work Step by Step

Applying the Distributive Property, multiply each term in the second set of parentheses with $3x-4$: $(3x-4)(3x^3)=(3x)(3x^3)+(-4)(3x^3)=9x^4-12x^3\\(3x-4)(2x^2)=(3x)(2x^2)+(-4)(2x^2)=6x^3-8x^2\\(3x-4)(-8)=(3x)(-8)+(-4)(3-8)=-24x+32$ Thus, $(3x-4)(3x^3)+(3x-4)(2x^2)+(3x-4)(-8)\\=9x^4-12x^3+6x^3-8x^2-24x+32\\=9x^4-6x^3-8x^2-24x+32$
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