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: 106

Answer

$(x^n-2)(3x^n-2)$

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: $\\=(x^n-2)(3x^n-2)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.