Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set - Page 304: 106



Work Step by Step

The product of the leading coefficient and the constant term is $3(4)=12$. The factors of 12 whose sum is equal to the coefficient of the middle term (which is -8) are $-6$ and $-2$. Rewrite the middle term using these factors to have: $\\3x^{2n}-8x^n+4 \\=3x^{2n}-6x^n-2x^n+4 \\=(3x^{2n}-6x^n) + (-2x^n+4)$ Factor out the GCF of each group to have: $\\=3x^n(x^n-2)+(-2)(x^n-2)$ Factor out the GCF of $x^n-2$ to have: $\\=(x^n-2)(3x^n-2)$
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