Algebra 1

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

Chapter 8 - Polynomials and Factoring - 8-8 Factoring by Grouping - Practice and Problem-Solving Exercises: 35

Answer

$4x(x+3)(x^{2} +2)$

Work Step by Step

The polynomial have a common factor of 4x therefore factor out the 4x from all four terms. $4x( x^{3} + 3x^{2} + 2x + 6)$ Group the first two terms and last two terms together $4x( (x^{3} + 3x^{2}) +(2x + 6))$ Factor out the GCF from the first two terms and last two terms $4x( x^{2} (x+3) +2(x + 3))$ The student made the mistake that they only factored out the 4 and not the x from the first four terms. $4x( x^{2} (x+3) +2(x + 3))$ Take out (x+3) common factor and that gives us $4x(x+3)(x^{2} +2)$
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