## Intermediate Algebra (12th Edition)

$(z+1) \left( 3z-1 \right)$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $(z+1)(z-4)+(z+1)(2z+3) ,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. $\bf{\text{Solution Details:}}$ Factoring the $GCF= z+1 ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (z+1) \left( \dfrac{(z+1)(z-4)}{z+1}+\dfrac{(z+1)(2z+3)}{z+1} \right) \\\\= (z+1) \left( (z-4)+(2z+3) \right) \\\\= (z+1) \left( z-4+2z+3 \right) \\\\= (z+1) \left( 3z-1 \right) .\end{array}