Question

solve by factoring.
$3m^2 - 17m - 56 = 0$

$m = \square$ (use a comma to separate answers as needed.)

Explanation:

Step1: Factor the quadratic trinomial

We need two numbers that multiply to $3\times(-56)=-168$ and add to $-17$. These numbers are $-24$ and $7$. Rewrite and factor:
$$3m^2 -24m +7m -56=0$$
$$3m(m-8)+7(m-8)=0$$
$$(3m+7)(m-8)=0$$

Step2: Apply zero product property

Set each factor equal to 0:
$3m+7=0$ or $m-8=0$

Step3: Solve for $m$

For $3m+7=0$: $3m=-7 \implies m=-\frac{7}{3}$
For $m-8=0$: $m=8$

Answer:

$-\frac{7}{3}, 8$