# Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 49

$-a^4(a+15)(a-6)$

#### Work Step by Step

Factoring the negative $GCF= -a^4$, the given expression, $-a^6-9a^5+90a^4 ,$ is equivalent to \begin{array}{l} -a^4(a^2+9a-90) .\end{array} The 2 numbers whose product is $ac= 1(-90)=-90$ and whose sum is $b= 9$ are $\left\{ 15,-6 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} -a^4(a^2+15a-6a-90) \\\\= -a^4[(a^2+15a)-(6a+90)] \\\\= -a^4[a(a+15)-6(a+15)] \\\\= -a^4[(a+15)(a-6)] \\\\= -a^4(a+15)(a-6) .\end{array}

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