College Algebra 7th Edition

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

Chapter P, Prerequisites - Section P.6 - Factoring - P.6 Exercises: 17

Answer

$(x+5)(x-3)$

Work Step by Step

RECALL: A trinomial of the form $x^2+bx+c$ (leading coefficient is 1) can be factored if there are factors of $c$ (say, $d$ and $e$) whose sum is equal to $b$. The trinomial factors as $(x+d)(x+e)$ The given trinomial has a leading coefficient of 1 so the factoring technique mentioned above may be used. Look for factors of $-15$ whose sum is equal to $2$. Note that $(5)(-3)) = -15$ and $5+(-3)=2$ This means that the given trinomial factors as $(x+5)[x+(-3)]= (x+5)(x-3)$.
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