Solve x^2+9x+3x+27

$$x ^ { 2 } + 9 x + 3 x + 27$$

Factor

$$\left(x+3\right)\left(x+9\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+12x+27$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+27. To find a and b, set up a system to be solved.

$$a+b=12 ab=1\times 27=27$$

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 27.

$$1,27 3,9$$

Calculate the sum for each pair.

$$1+27=28 3+9=12$$

The solution is the pair that gives sum 12.

$$a=3 b=9$$

Rewrite x^{2}+12x+27 as \left(x^{2}+3x\right)+\left(9x+27\right).

$$\left(x^{2}+3x\right)+\left(9x+27\right)$$

Factor out x in the first and 9 in the second group.

$$x\left(x+3\right)+9\left(x+3\right)$$

Factor out common term x+3 by using distributive property.

$$\left(x+3\right)\left(x+9\right)$$

Evaluate

$$\left(x+3\right)\left(x+9\right)$$

Solution Steps

Combine 9x and 3x to get 12x.

$$x^{2}+12x+27$$