Solve x^2+4x-6x-24

$$x ^ { 2 } + 4 x - 6 x - 24$$

Factor

$$\left(x-6\right)\left(x+4\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-2x-24$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-24. To find a and b, set up a system to be solved.

$$a+b=-2 ab=1\left(-24\right)=-24$$

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 -24.

$$1,-24 2,-12 3,-8 4,-6$$

Calculate the sum for each pair.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

The solution is the pair that gives sum -2.

$$a=-6 b=4$$

Rewrite x^{2}-2x-24 as \left(x^{2}-6x\right)+\left(4x-24\right).

$$\left(x^{2}-6x\right)+\left(4x-24\right)$$

Factor out x in the first and 4 in the second group.

$$x\left(x-6\right)+4\left(x-6\right)$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x+4\right)$$

Evaluate

$$\left(x-6\right)\left(x+4\right)$$

Solution Steps

Combine 4x and -6x to get -2x.

$$x^{2}-2x-24$$