Answer
$(y-3)(y+10)$
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, $
y^2+7y-30
,$ the value of $c$ is $
-30
$ and the value of $b$ is $
7
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,-30 \}, \{ 2,-15 \}, \{ 3,-10 \}, \{ 5,-6 \},
\{ -1,30 \}, \{ -2,15 \}, \{ -3,10 \}, \{ -5,6 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
-3,10
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
(y-3)(y+10)
.\end{array}
