Solve 5k^3+20k^2-15

$$5 k ^ { 3 } + 20 k ^ { 2 } - 15$$

Factor

$$5\left(k+1\right)\left(k^{2}+3k-3\right)$$

Solution Steps

Factor out 5.

$$5\left(k^{3}+4k^{2}-3\right)$$

Consider k^{3}+4k^{2}-3. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -3 and q divides the leading coefficient 1. One such root is -1. Factor the polynomial by dividing it by k+1.

$$\left(k+1\right)\left(k^{2}+3k-3\right)$$

Rewrite the complete factored expression. Polynomial k^{2}+3k-3 is not factored since it does not have any rational roots.

$$5\left(k+1\right)\left(k^{2}+3k-3\right)$$

Evaluate

$$5\left(k^{3}+4k^{2}-3\right)$$