Solve 3f^3-9f^2+11f-33

$$3 f ^ { 3 } - 9 f ^ { 2 } + 11 f - 33$$

Factor

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

Solution Steps

Do the grouping 3f^{3}-9f^{2}+11f-33=\left(3f^{3}-9f^{2}\right)+\left(11f-33\right), and factor out 3f^{2} in the first and 11 in the second group.

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

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

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

Evaluate

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