Solve 3x^2-6x+4x-8

$$3 x ^ { 2 } - 6 x + 4 x - 8$$

Factor

$$\left(x-2\right)\left(3x+4\right)$$

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx-8. To find a and b, set up a system to be solved.

$$a+b=-2 ab=3\left(-8\right)=-24$$

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 3x^{2}-2x-8 as \left(3x^{2}-6x\right)+\left(4x-8\right).

$$\left(3x^{2}-6x\right)+\left(4x-8\right)$$

Factor out 3x in the first and 4 in the second group.

$$3x\left(x-2\right)+4\left(x-2\right)$$

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

$$\left(x-2\right)\left(3x+4\right)$$

Evaluate

$$\left(x-2\right)\left(3x+4\right)$$

Solution Steps

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

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