Solve f^3-4f^2-9f+36

$$f ^ { 3 } - 4 f ^ { 2 } - 9 f + 36$$

Factor

$$\left(f-4\right)\left(f-3\right)\left(f+3\right)$$

Solution Steps

Do the grouping f^{3}-4f^{2}-9f+36=\left(f^{3}-4f^{2}\right)+\left(-9f+36\right), and factor out f^{2} in the first and -9 in the second group.

$$f^{2}\left(f-4\right)-9\left(f-4\right)$$

Factor out common term f-4 by using distributive property.

$$\left(f-4\right)\left(f^{2}-9\right)$$

Consider f^{2}-9. Rewrite f^{2}-9 as f^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(f-3\right)\left(f+3\right)$$

Rewrite the complete factored expression.

$$\left(f-4\right)\left(f-3\right)\left(f+3\right)$$

Evaluate

$$\left(f-4\right)\left(f^{2}-9\right)$$