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

$-2t(t+2)(t+3)$
Factoring the negative $GCF= -2t ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} -2t^3-10t^2-12t \\\\= -2t(t^2+5t+6) .\end{array} Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} -2t(t^2+5t+6) \end{array} has $c= 6$ and $b= 5 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 2,3 \right\}.$ Using these two numbers, the $\text{ expression }$ above is equivalent to \begin{array}{l}\require{cancel} -2t(t+2)(t+3) .\end{array}