Answer
$(x+z)(x+7z)$
Work Step by Step
The two numbers whose product is $ac=
1(7)=7
$ and whose sum is $b=
8
$ are $\{
1,7
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
x^2+8xz+7z^2
$, is
\begin{array}{l}\require{cancel}
x^2+xz+7xz+7z^2
\\\\=
(x^2+xz)+(7xz+7z^2)
\\\\=
x(x+z)+7z(x+z)
\\\\=
(x+z)(x+7z)
.\end{array}
