## Algebra 1: Common Core (15th Edition)

$(3x+1)(x+5)$
Find factors of $ac$ that have a sum of $b$. Since $ac=15$ and $b=16$, find factors of $15$ with a sum of $16$. $\left[\begin{array}{lll} \text{Factors of 15 } & \text{Sum of factors} & \\ 1\text{ and }15 & 16 & \text{...what we need} \end{array}\right]$ $3x^{2}+16x+5$ ...use the factors to rewrite $bx$. $=3x^{2}+x+15x+5$ ...factor out the GCF out of each pair of terms. $=x(3x+1)+5(3x+1)$ ...use the Distributive Property. $=(3x+1)(x+5)$