Simplify (6m^3-16m^2+15m-40)/(2m^2+5)

$\frac{6 m^{3} - 16 m^{2} + 15 m - 40}{2 m^{2} + 5}$

Step 1

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(6 m^{3} - 16 m^{2}) + 15 m - 40}{2 m^{2} + 5}$

Factor out the greatest common factor (GCF) from each group.

$\frac{2 m^{2} (3 m - 8) + 5 (3 m - 8)}{2 m^{2} + 5}$

Factor the polynomial by factoring out the greatest common factor, $3 m - 8$ .

$\frac{(3 m - 8) (2 m^{2} + 5)}{2 m^{2} + 5}$

Step 2

Cancel the common factor of $2 m^{2} + 5$ .

Cancel the common factor.

$\frac{(3 m - 8) (2 m^{2} + 5)}{2 m^{2} + 5}$

Divide $3 m - 8$ by $1$ .

$3 m - 8$