Solve (x^2+6x+8)+(x+2)

$$( x ^ { 2 } + 6 x + 8 ) + ( x + 2 )$$

Evaluate

$$\left(x+2\right)\left(x+5\right)$$

Solution Steps

Combine 6x and x to get 7x.

$$x^{2}+7x+8+2$$

Add 8 and 2 to get 10.

$$x^{2}+7x+10$$

Factor

$$\left(x+2\right)\left(x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+7x+10$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+10. To find a and b, set up a system to be solved.

$$a+b=7 ab=1\times 10=10$$

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 10.

$$1,10 2,5$$

Calculate the sum for each pair.

$$1+10=11 2+5=7$$

The solution is the pair that gives sum 7.

$$a=2 b=5$$

Rewrite x^{2}+7x+10 as \left(x^{2}+2x\right)+\left(5x+10\right).

$$\left(x^{2}+2x\right)+\left(5x+10\right)$$

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

$$x\left(x+2\right)+5\left(x+2\right)$$

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

$$\left(x+2\right)\left(x+5\right)$$