Solve x^3+6x^2+8x

$$x ^ { 3 } + 6 x ^ { 2 } + 8 x$$

Factor

$$x\left(x+2\right)\left(x+4\right)$$

Solution Steps

Factor out x.

$$x\left(x^{2}+6x+8\right)$$

Consider x^{2}+6x+8. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+8. To find a and b, set up a system to be solved.

$$a+b=6 ab=1\times 8=8$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 8.

$$1,8 2,4$$

Calculate the sum for each pair.

$$1+8=9 2+4=6$$

The solution is the pair that gives sum 6.

$$a=2 b=4$$

Rewrite x^{2}+6x+8 as \left(x^{2}+2x\right)+\left(4x+8\right).

$$\left(x^{2}+2x\right)+\left(4x+8\right)$$

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

$$x\left(x+2\right)+4\left(x+2\right)$$

Factor out common term x+2 by using distributive property.

$$\left(x+2\right)\left(x+4\right)$$

Rewrite the complete factored expression.

$$x\left(x+2\right)\left(x+4\right)$$

Evaluate

$$x\left(x+2\right)\left(x+4\right)$$