Solve x^2+3x-8x-24

$$x ^ { 2 } + 3 x - 8 x - 24$$

Factor

$$\left(x-8\right)\left(x+3\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-5x-24$$

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.

$$a+b=-5 ab=1\left(-24\right)=-24$$

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 -5.

$$a=-8 b=3$$

Rewrite x^{2}-5x-24 as \left(x^{2}-8x\right)+\left(3x-24\right).

$$\left(x^{2}-8x\right)+\left(3x-24\right)$$

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

$$x\left(x-8\right)+3\left(x-8\right)$$

Factor out common term x-8 by using distributive property.

$$\left(x-8\right)\left(x+3\right)$$

Evaluate

$$\left(x-8\right)\left(x+3\right)$$

Solution Steps

Combine 3x and -8x to get -5x.

$$x^{2}-5x-24$$