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

$(3t+7)(t+3)$
The $2$ numbers whose product is $ac= 3(21)=63$ and whose sum is $b= 16$ are ${ 7,9 }.$ Using these $2$ numbers to decompose the middle term of the given expression, $3t^2+16t+21 ,$ then the factored form is \begin{array}{l} 3t^2+7t+9t+21 \\\\= (3t^2+7t)+(9t+21) \\\\= t(3t+7)+3(3t+7) \\\\= (3t+7)(t+3) .\end{array}