Solve (D^3-D^2-8D+12)

$$( D ^ { 3 } - D ^ { 2 } - 8 D + 12 )$$

Factor

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

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 D+3.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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