## Intermediate Algebra (12th Edition)

$(y-3)(y+10)$
$\bf{\text{Solution Outline:}}$ 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}
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