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

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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:

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