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 - Page 269: 68



Work Step by Step

We do this problem like we did with the FOIL method. However, there now may be more than two terms per factor, so we cannot just multiply the first, outer, inner, and last terms together. Instead, we must be sure that all terms within both factors are multiplied by each other. Doing this, we find: $$\left(x^2-3x+2\right)\left(x^2+x+1\right) \\ x^2x^2+x^2x+x^2\cdot \:1+\left(-3x\right)x^2+\left(-3x\right)x+\left(-3x\right)\cdot \:1+2x^2+2x+2\cdot \:1 \\ x^4-2x^3-x+2$$
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