Solve 12x^3-60x^2-12x+60

$$12 x ^ { 3 } - 60 x ^ { 2 } - 12 x + 60$$

Factor

$$12\left(x-5\right)\left(x-1\right)\left(x+1\right)$$

Solution Steps

Factor out 12.

$$12\left(x^{3}-5x^{2}-x+5\right)$$

Consider x^{3}-5x^{2}-x+5. Do the grouping x^{3}-5x^{2}-x+5=\left(x^{3}-5x^{2}\right)+\left(-x+5\right), and factor out x^{2} in the first and -1 in the second group.

$$x^{2}\left(x-5\right)-\left(x-5\right)$$

Factor out common term x-5 by using distributive property.

$$\left(x-5\right)\left(x^{2}-1\right)$$

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.

$$12\left(x-5\right)\left(x-1\right)\left(x+1\right)$$

Evaluate

$$12\left(x-5\right)\left(x^{2}-1\right)$$