One root of the quadratic polynomial $ax^2+13x-6$ is equal to $-3$. Which of the following binomials is a factor of $ax^2+13x-6$ ?

$x-\dfrac{2}{5}$

$x+\dfrac{2}{5}$

$x-3$

$x-5$

$x+5$

Approach

If $x=-3$ is a root, the polynomial must have an $x$-intercept at $x=-3$.

$$ ax^2+13x-6 =0 $$ $$ a(-3)^2+13(-3)-6 =0 $$ $$ 9a-39-6 = 0 $$ $$ 9a=45 $$ $$ a=5 $$

We can factor the resulting quadratic normally:

$$ 5x^2+13x-6 =0 $$ $$ (5x-2)(x+3)=0 $$ $$ 5\left(x-\frac{2}{5}\right)(x+3)=0 $$