College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Chapter P Review - Exercises: 68

Answer

$(a+b-5)(a+b+2)$

Work Step by Step

If we let $u=a+b$, the given expression becomes: $=u^2-3u-10$ 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 trinomial in the expression above has $a=1, b=-3$, and $c=-10$. Note that $-10=-5(2)$ and $-3 = -5+2$. This means that $d=-5$ and $e=2$ Thus, the factored form of the trinomial is: $=[u+(-5)][u+2] = (u-5)(u+2)$ Replace $u$ with its equivalent $a+b$ to otain: $=[(a+b)-5][(a+b+2] \\=(a+b-5)(a+b+2)$
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