Question

Determine whether $3x+2$ is a factor of $6x^2+13x+6$.

Answer 1

Let $p\left(x\right)=$ $6x^2+13x+6$
By the factor theorem, $3x+2$ is a factor of $p\left(x\right)$, if $p\left(\frac{-2}{3}\right)=0$
Find the value of $p\left(\frac{-2}{3}\right)$
$p\left(x\right)=6x^2+13x+6$
$p\left(\frac{-2}{3}\right)=6{\left(\frac{-2}{3}\right)}^2+13\left(\frac{-2}{3}\right)+6$
$0=6\times \frac{4}{9}-\frac{26}{3}+6$
$0=\frac{8}{3}-\frac{26}{3}+6$
$0=\frac{-18}{3}+6$
$0=-6+6$
$0=0$
Therefore, $3x+2$ is a factor of $p\left(x\right)$.