Answer
a. $(2x+1)(3x+5)$
b. The factors are both negative.
Work Step by Step
a. Find factors of $ac$ that have a sum of $b$.
Since $ac=30$ and $b=13$,
find positive factors of $30$ with a sum of $13$.
$\left[\begin{array}{lll}
\text{Factors of 30 } & \text{Sum of factors} & \\
1\text{ and }30 & 31 & \\
2\text{ and }15 & 17 & \\
3\text{ and }10 & 13 & \text{is what we need}
\end{array}\right]$
$6x^{2}+13x+5$
...use the factors to rewrite $bx$.
$=6x^{2}+3x+10x+5$
...factor out the GCF out of each pair of terms.
$=3x(2x+1)+5(2x+1)$
...use the Distributive Property.
$=(2x+1)(3x+5)$
---
b.
The factors are both negative.
In order to have a positive product both factors must be either positive or negative.
In this case, $b$ is negative, so $a $ and $c$ must give a negative sum and a positive product.
