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

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

Factor

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

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.

$$a+b=10 ab=8\times 3=24$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 24.

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

Calculate the sum for each pair.

$$1+24=25 2+12=14 3+8=11 4+6=10$$

The solution is the pair that gives sum 10.

$$a=4 b=6$$

Rewrite 8x^{2}+10x+3 as \left(8x^{2}+4x\right)+\left(6x+3\right).

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

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

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

Factor out common term 2x+1 by using distributive property.

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

Evaluate

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

Solution Steps

Combine 6x and 4x to get 10x.

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