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

$2t^2(s^3+2t)(s^3+3t)$
Factoring the $GCF= 2t^2$, then the given expression, $2s^6t^2+10s^3t^3+12t^4$ is equivalent to \begin{array}{l} 2t^2(s^6+5s^3t+6t^2) .\end{array} The two numbers whose product is $ac= 1(6)=6$ and whose sum is $b= 5$ are $\{ 2,3 \}$. Using these two numbers to decompose the middle term of the expression, $2t^2(s^6+5s^3t+6t^2) ,$ then the factored form is \begin{array}{l} 2t^2(s^6+2s^3t+3s^3t+6t^2) \\\\= 2t^2[(s^6+2s^3t)+(3s^3t+6t^2)] \\\\= 2t^2[s^3(s^3+2t)+3t(s^3+2t)] \\\\= 2t^2[(s^3+2t)(s^3+3t)] \\\\= 2t^2(s^3+2t)(s^3+3t) .\end{array}