Solve m^3-12m+16

$$m ^ { 3 } - 12 m + 16$$

Factor

$$\left(m+4\right)\left(m-2\right)^{2}$$

Solution Steps

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 16 and q divides the leading coefficient 1. One such root is -4. Factor the polynomial by dividing it by m+4.

$$\left(m+4\right)\left(m^{2}-4m+4\right)$$

Consider m^{2}-4m+4. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=m and b=2.

$$\left(m-2\right)^{2}$$

Rewrite the complete factored expression.

$$\left(m+4\right)\left(m-2\right)^{2}$$

Evaluate

$$\left(m+4\right)\left(m-2\right)^{2}$$