Solve x^2+8x+4x+32

$$x ^ { 2 } + 8 x + 4 x + 32$$

Factor

$$\left(x+4\right)\left(x+8\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+12x+32$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+32. To find a and b, set up a system to be solved.

$$a+b=12 ab=1\times 32=32$$

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 32.

$$1,32 2,16 4,8$$

Calculate the sum for each pair.

$$1+32=33 2+16=18 4+8=12$$

The solution is the pair that gives sum 12.

$$a=4 b=8$$

Rewrite x^{2}+12x+32 as \left(x^{2}+4x\right)+\left(8x+32\right).

$$\left(x^{2}+4x\right)+\left(8x+32\right)$$

Factor out x in the first and 8 in the second group.

$$x\left(x+4\right)+8\left(x+4\right)$$

Factor out common term x+4 by using distributive property.

$$\left(x+4\right)\left(x+8\right)$$

Evaluate

$$\left(x+4\right)\left(x+8\right)$$

Solution Steps

Combine 8x and 4x to get 12x.

$$x^{2}+12x+32$$