Solve 12x^2+15x+8x+10

$$12 x ^ { 2 } + 15 x + 8 x + 10$$

Factor

$$\left(3x+2\right)\left(4x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$12x^{2}+23x+10$$

Factor the expression by grouping. First, the expression needs to be rewritten as 12x^{2}+ax+bx+10. To find a and b, set up a system to be solved.

$$a+b=23 ab=12\times 10=120$$

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 120.

$$1,120 2,60 3,40 4,30 5,24 6,20 8,15 10,12$$

Calculate the sum for each pair.

$$1+120=121 2+60=62 3+40=43 4+30=34 5+24=29 6+20=26 8+15=23 10+12=22$$

The solution is the pair that gives sum 23.

$$a=8 b=15$$

Rewrite 12x^{2}+23x+10 as \left(12x^{2}+8x\right)+\left(15x+10\right).

$$\left(12x^{2}+8x\right)+\left(15x+10\right)$$

Factor out 4x in the first and 5 in the second group.

$$4x\left(3x+2\right)+5\left(3x+2\right)$$

Factor out common term 3x+2 by using distributive property.

$$\left(3x+2\right)\left(4x+5\right)$$

Evaluate

$$\left(3x+2\right)\left(4x+5\right)$$

Solution Steps

Combine 15x and 8x to get 23x.

$$12x^{2}+23x+10$$