Solve 8x^2-2x+12x-3

$$8 x ^ { 2 } - 2 x + 12 x - 3$$

Factor

$$\left(4x-1\right)\left(2x+3\right)$$

Solution Steps

Multiply and combine like terms.

$$8x^{2}+10x-3$$

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

$$a+b=10 ab=8\left(-3\right)=-24$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. 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 10.

$$a=-2 b=12$$

Rewrite 8x^{2}+10x-3 as \left(8x^{2}-2x\right)+\left(12x-3\right).

$$\left(8x^{2}-2x\right)+\left(12x-3\right)$$

Factor out 2x in the first and 3 in the second group.

$$2x\left(4x-1\right)+3\left(4x-1\right)$$

Factor out common term 4x-1 by using distributive property.

$$\left(4x-1\right)\left(2x+3\right)$$

Evaluate

$$\left(4x-1\right)\left(2x+3\right)$$

Solution Steps

Combine -2x and 12x to get 10x.

$$8x^{2}+10x-3$$