Solve P(x)=x^3-7x^2-x+7

$$P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - x + 7$$

Factor

$$\left(x-7\right)\left(x-1\right)\left(x+1\right)$$

Solution Steps

Do the grouping x^{3}-7x^{2}-x+7=\left(x^{3}-7x^{2}\right)+\left(-x+7\right), and factor out x^{2} in the first and -1 in the second group.

$$x^{2}\left(x-7\right)-\left(x-7\right)$$

Factor out common term x-7 by using distributive property.

$$\left(x-7\right)\left(x^{2}-1\right)$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$\left(x-7\right)\left(x-1\right)\left(x+1\right)$$

Evaluate

$$\left(x-7\right)\left(x^{2}-1\right)$$