Solve h(t)=t^3+8t^2+13t+6

$$h ( t ) = t ^ { 3 } + 8 t ^ { 2 } + 13 t + 6$$

Factor

$$\left(t+6\right)\left(t+1\right)^{2}$$

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 6 and q divides the leading coefficient 1. One such root is -6. Factor the polynomial by dividing it by t+6.

$$\left(t+6\right)\left(t^{2}+2t+1\right)$$

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

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

Rewrite the complete factored expression.

$$\left(t+6\right)\left(t+1\right)^{2}$$

Evaluate

$$\left(t+6\right)\left(t+1\right)^{2}$$