Solve x^3+x^2-8x-12

$$x ^ { 3 } + x ^ { 2 } - 8 x - 12$$

Factor

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

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 -12 and q divides the leading coefficient 1. One such root is 3. Factor the polynomial by dividing it by x-3.

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

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

$$\left(x+2\right)^{2}$$

Rewrite the complete factored expression.

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

Evaluate

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