College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.5 - Factoring Polynomials - R.5 Assess Your Understanding: 45

Answer

$(x+6)(x+1)$

Work Step by Step

RECALL: A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$. The trinomial's factored form will be: $x^2+bx+c=(x+d)(x+e)$ The given trinomial has $b=7$ and $c=6$. Note that $6=6(1)$ and $7=6+1$. This means that $d=6$ and $e=1$ Thus, the factored form of the trinomial is: $(x+6)(x+1)$
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