Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 8 - Polynomials and Factoring - 8-4 Multiplying Special Cases - Mixed Review: 69

Answer

6x(2$x^{3}$+5$x^{2}$+7)

Work Step by Step

In order to factor 12$x^{4}$+30$x^{3}$+42x we will look for the greatest factor that exists in each term, and factor out what's known as the GCF (Greatest common factor). In this case, the GCF is 6x, because it's the greatest factor that factors out of all three terms. After we factor out the 6x, we'll leave in parentheses whatever multiplies to the corresponding term in the original equation. For example, for the first term, after we factor out the 6x, we'll leave a 2$x^{3}$ because 6x multiplied by 2$x^{3}$ equals 12$x^{4}$. We'll end up rewriting the polynomial as 6x(2$x^{3}$+5$x^{2}$+7)
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