Answer
$(z+3w)(z+5w)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the quadratic expression $x^2+bx+c,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$. Then, express the factored form as $(x+m_1)(x+m_2).$
$\bf{\text{Solution Details:}}$
In the given expression, $
z^2+8zw+15w^2
,$ the value of $c$ is $
15
$ and the value of $b$ is $
8
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{1,15\}, \{3,5\},
\{-1,-15\}, \{-3,-5\}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
3,5
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
(z+3w)(z+5w)
.\end{array}
