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: 67

Answer

$(x+y-6)(x+y-1)$

Work Step by Step

If we let $u=x+y$, the given expression becomes: $=u^2-7u+6$ 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 $a=1, b=-7$, 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: $[u+(-6)][u(-1] = (u-)(u-1)$ Replace $u$ with its equivalent $x+y$ to otain: $=[(x+y)-6][(x+y-1] \\=(x+y-6)(x+y-1)$
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