Solve 5x^3+5x^2-60x

$$5 x ^ { 3 } + 5 x ^ { 2 } - 60 x$$

Factor

$$5x\left(x-3\right)\left(x+4\right)$$

Solution Steps

Factor out 5.

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

Consider x^{3}+x^{2}-12x. Factor out x.

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

Consider x^{2}+x-12. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-12. To find a and b, set up a system to be solved.

$$a+b=1 ab=1\left(-12\right)=-12$$

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 -12.

$$-1,12 -2,6 -3,4$$

Calculate the sum for each pair.

$$-1+12=11 -2+6=4 -3+4=1$$

The solution is the pair that gives sum 1.

$$a=-3 b=4$$

Rewrite x^{2}+x-12 as \left(x^{2}-3x\right)+\left(4x-12\right).

$$\left(x^{2}-3x\right)+\left(4x-12\right)$$

Factor out x in the first and 4 in the second group.

$$x\left(x-3\right)+4\left(x-3\right)$$

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

$$\left(x-3\right)\left(x+4\right)$$

Rewrite the complete factored expression.

$$5x\left(x-3\right)\left(x+4\right)$$

Evaluate

$$5x\left(x-3\right)\left(x+4\right)$$