Solve x^3-x^2-30x

$$x ^ { 3 } - x ^ { 2 } - 30 x$$

Factor

$$x\left(x-6\right)\left(x+5\right)$$

Solution Steps

Factor out x.

$$x\left(x^{2}-x-30\right)$$

Consider x^{2}-x-30. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-30. To find a and b, set up a system to be solved.

$$a+b=-1 ab=1\left(-30\right)=-30$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -30.

$$1,-30 2,-15 3,-10 5,-6$$

Calculate the sum for each pair.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

The solution is the pair that gives sum -1.

$$a=-6 b=5$$

Rewrite x^{2}-x-30 as \left(x^{2}-6x\right)+\left(5x-30\right).

$$\left(x^{2}-6x\right)+\left(5x-30\right)$$

Factor out x in the first and 5 in the second group.

$$x\left(x-6\right)+5\left(x-6\right)$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x+5\right)$$

Rewrite the complete factored expression.

$$x\left(x-6\right)\left(x+5\right)$$

Evaluate

$$x\left(x-6\right)\left(x+5\right)$$