Solve 4x^3+24x^2+20x

$$4 x ^ { 3 } + 24 x ^ { 2 } + 20 x$$

Factor

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

Solution Steps

Factor out 4.

$$4\left(x^{3}+6x^{2}+5x\right)$$

Consider x^{3}+6x^{2}+5x. Factor out x.

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

Consider x^{2}+6x+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.

$$a+b=6 ab=1\times 5=5$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=1 b=5$$

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

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

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

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

Factor out common term x+1 by using distributive property.

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

Rewrite the complete factored expression.

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

Evaluate

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