Solve x^2-12x+3x-36

$$x ^ { 2 } - 12 x + 3 x - 36$$

Factor

$$\left(x-12\right)\left(x+3\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-9x-36$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-36. To find a and b, set up a system to be solved.

$$a+b=-9 ab=1\left(-36\right)=-36$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -36.

$$1,-36 2,-18 3,-12 4,-9 6,-6$$

Calculate the sum for each pair.

$$1-36=-35 2-18=-16 3-12=-9 4-9=-5 6-6=0$$

The solution is the pair that gives sum -9.

$$a=-12 b=3$$

Rewrite x^{2}-9x-36 as \left(x^{2}-12x\right)+\left(3x-36\right).

$$\left(x^{2}-12x\right)+\left(3x-36\right)$$

Factor out x in the first and 3 in the second group.

$$x\left(x-12\right)+3\left(x-12\right)$$

Factor out common term x-12 by using distributive property.

$$\left(x-12\right)\left(x+3\right)$$

Evaluate

$$\left(x-12\right)\left(x+3\right)$$

Solution Steps

Combine -12x and 3x to get -9x.

$$x^{2}-9x-36$$