The first we are going to do to simplify the expression [tex] \frac{6m^{3}-16m^{2}+15m-40}{2m^2+5} [/tex] is factoring the numerator by grouping similar terms as follows:
[tex] \frac{6m^{3}-16m^{2}+15m-40}{2m^2+5} [/tex]
[tex]\frac{(6m^{3}-16m^{2})+(15m-40)}{2m^2+5} [/tex]
[tex]\frac{2m^2(3m-8)+5(3m-8)}{2m^2+5} [/tex]
[tex]\frac{(3m-8)(2m^2+5)}{2m^2+5}[/tex]
Now we can cancel the common factor, [tex]2m^2+5[/tex] in both numerator and denominator:
[tex]\frac{(3m-8)(2m^2+5)}{2m^2+5}[/tex]
[tex]3m-8[/tex]
We can conclude that [tex]\frac{6m^{3}-16m^{2}+15m-40}{2m^2+5} =3m-8[/tex]
