Answer
$(2z+7)^2$
Work Step by Step
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}
