Solve =m^3-3m+2

$$= m ^ { 3 } - 3 m + 2$$

Factor

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

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 2 and q divides the leading coefficient 1. One such root is -2. Factor the polynomial by dividing it by m+2.

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

Consider m^{2}-2m+1. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=m and b=1.

$$\left(m-1\right)^{2}$$

Rewrite the complete factored expression.

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

Evaluate

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