Solve x^2+8x+5x+40=

$$x ^ { 2 } + 8 x + 5 x + 40 =$$

Factor

$$\left(x+5\right)\left(x+8\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+13x+40$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+40. To find a and b, set up a system to be solved.

$$a+b=13 ab=1\times 40=40$$

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 40.

$$1,40 2,20 4,10 5,8$$

Calculate the sum for each pair.

$$1+40=41 2+20=22 4+10=14 5+8=13$$

The solution is the pair that gives sum 13.

$$a=5 b=8$$

Rewrite x^{2}+13x+40 as \left(x^{2}+5x\right)+\left(8x+40\right).

$$\left(x^{2}+5x\right)+\left(8x+40\right)$$

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

$$x\left(x+5\right)+8\left(x+5\right)$$

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

$$\left(x+5\right)\left(x+8\right)$$

Evaluate

$$\left(x+5\right)\left(x+8\right)$$

Solution Steps

Combine 8x and 5x to get 13x.

$$x^{2}+13x+40$$