Solve 4x^3-16x^2-20x

$$4 x ^ { 3 } - 16 x ^ { 2 } - 20 x$$

Factor

$$4x\left(x-5\right)\left(x+1\right)$$

Solution Steps

Factor out 4.

$$4\left(x^{3}-4x^{2}-5x\right)$$

Consider x^{3}-4x^{2}-5x. Factor out x.

$$x\left(x^{2}-4x-5\right)$$

Consider x^{2}-4x-5. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-5. To find a and b, set up a system to be solved.

$$a+b=-4 ab=1\left(-5\right)=-5$$

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. The only such pair is the system solution.

$$a=-5 b=1$$

Rewrite x^{2}-4x-5 as \left(x^{2}-5x\right)+\left(x-5\right).

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

Factor out x in x^{2}-5x.

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

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

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

Rewrite the complete factored expression.

$$4x\left(x-5\right)\left(x+1\right)$$

Evaluate

$$4x\left(x-5\right)\left(x+1\right)$$