Solve x^3+11x^2-3x-33

$$x ^ { 3 } + 11 x ^ { 2 } - 3 x - 33$$

Factor

$$\left(x+11\right)\left(x^{2}-3\right)$$

Solution Steps

Do the grouping x^{3}+11x^{2}-3x-33=\left(x^{3}+11x^{2}\right)+\left(-3x-33\right), and factor out x^{2} in the first and -3 in the second group.

$$x^{2}\left(x+11\right)-3\left(x+11\right)$$

Factor out common term x+11 by using distributive property. Polynomial x^{2}-3 is not factored since it does not have any rational roots.

$$\left(x+11\right)\left(x^{2}-3\right)$$

Evaluate

$$\left(x+11\right)\left(x^{2}-3\right)$$