## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$6a^{8}(a+7)(a-2)$
Factoring the $GCF= 6a^8$, the given expression, $6a^{10}+30a^9-84a^8 ,$ is equivalent to \begin{array}{l} 6a^{8}(a^2+5a-14) .\end{array} The 2 numbers whose product is $ac= 1(-14)=-14$ and whose sum is $b= 5$ are $\left\{ 7,-2 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} 6a^{8}(a^2+7a-2a-14) \\\\= 6a^{8}[(a^2+7a)-(2a+14)] \\\\= 6a^{8}[a(a+7)-2(a+7)] \\\\= 6a^{8}[(a+7)(a-2)] \\\\= 6a^{8}(a+7)(a-2) .\end{array}