Solve x^3-3x^2-49x+147

$$x ^ { 3 } - 3 x ^ { 2 } - 49 x + 147$$

Factor

$$\left(x-7\right)\left(x-3\right)\left(x+7\right)$$

Solution Steps

Do the grouping x^{3}-3x^{2}-49x+147=\left(x^{3}-3x^{2}\right)+\left(-49x+147\right), and factor out x^{2} in the first and -49 in the second group.

$$x^{2}\left(x-3\right)-49\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(x^{2}-49\right)$$

Consider x^{2}-49. Rewrite x^{2}-49 as x^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-7\right)\left(x+7\right)$$

Rewrite the complete factored expression.

$$\left(x-7\right)\left(x-3\right)\left(x+7\right)$$

Evaluate

$$\left(x-3\right)\left(x^{2}-49\right)$$