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

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

Factor

$$2x\left(x-5\right)\left(x+6\right)$$

Solution Steps

Factor out 2.

$$2\left(x^{3}+x^{2}-30x\right)$$

Consider x^{3}+x^{2}-30x. 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 positive, the positive number has greater absolute value than the negative. 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.

$$a=-5 b=6$$

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

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

Factor out x in the first and 6 in the second group.

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

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

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

Rewrite the complete factored expression.

$$2x\left(x-5\right)\left(x+6\right)$$

Evaluate

$$2x\left(x-5\right)\left(x+6\right)$$