## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter P - Section P.5 - Factoring Polynomials - Exercise Set: 19

#### Answer

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

#### Work Step by Step

RECALL: A quadratic trinomial $x^2+bx+c$ (with a leading coefficient of 1) can be factored as a product of two binomials if $c$ has factors $d$ and $e$ whose sum is equal to the coefficient of the middle term ($b$). The factored form of the trinomial is $(x+d)(x+e)$. Example: $x^2+3x+2$ can be factored as a product of two binomials since $2=2(1)$ and $2+1=3$, the middle term's coefficient. The given trinomial has a leading coefficient of 1 and has $c=-15$. Note that $-15=-5(3)$ and $-5+3=-2$, the middle term's coefficient. Thus, the factored form of the trinomial is $(x-5)(x+3).$

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