Question

Simplify the expression below.

Answer 1

The first we are going to do to simplify the expression $\frac{6m^{3}-16m^{2}+15m-40}{2m^2+5}$ is factoring the numerator by grouping similar terms as follows:
$\frac{6m^{3}-16m^{2}+15m-40}{2m^2+5}$
$\frac{(6m^{3}-16m^{2})+(15m-40)}{2m^2+5}$
$\frac{2m^2(3m-8)+5(3m-8)}{2m^2+5}$
$\frac{(3m-8)(2m^2+5)}{2m^2+5}$

Now we can cancel the common factor, $2m^2+5$ in both numerator and denominator:
$\frac{(3m-8)(2m^2+5)}{2m^2+5}$
$3m-8$

We can conclude that $\frac{6m^{3}-16m^{2}+15m-40}{2m^2+5} =3m-8$