## College Algebra (11th Edition)

$(2z+7)^2$
The two numbers whose product is $ac= 4(49)=196$ and whose sum is $b= 28$ are $\{ 14,14 \}$. Using these two numbers to decompose the middle term of the expression, $4z^2+28z+49 ,$ then the factored form is \begin{array}{l}\require{cancel} 4z^2+14z+14z+49 \\\\= (4z^2+14z)+(14z+49) \\\\= 2z(2z+7)+7(2z+7) \\\\= (2z+7)(2z+7) \\\\= (2z+7)^2 .\end{array}