Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.5 Multiplication of Polynomials - 4.5 Exercise Set: 67

Answer

$x^4+4x^3-3x^2+16x-3$

Work Step by Step

Using the Distributive Property, the product of the given expression, $ (x^2+5x-1)(x^2-x+3) ,$ is \begin{array}{l}\require{cancel} x^2(x^2)+x^2(-x)+x^2(3)+5x(x^2)+5x(-x)+5x(3)-1(x^2)-1(-x)-1(3) \\\\= x^4-x^3+3x^2+5x^3-5x^2+15x-x^2+x-3 \\\\= x^4+(-x^3+5x^3)+(3x^2-5x^2-x^2)+(15x+x)-3 \\\\= x^4+4x^3-3x^2+16x-3 .\end{array}
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