Solve 3x^2+4x+18x+24

$$3 x ^ { 2 } + 4 x + 18 x + 24$$

Factor

$$\left(x+6\right)\left(3x+4\right)$$

Solution Steps

Multiply and combine like terms.

$$3x^{2}+22x+24$$

Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx+24. To find a and b, set up a system to be solved.

$$a+b=22 ab=3\times 24=72$$

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 72.

$$1,72 2,36 3,24 4,18 6,12 8,9$$

Calculate the sum for each pair.

$$1+72=73 2+36=38 3+24=27 4+18=22 6+12=18 8+9=17$$

The solution is the pair that gives sum 22.

$$a=4 b=18$$

Rewrite 3x^{2}+22x+24 as \left(3x^{2}+4x\right)+\left(18x+24\right).

$$\left(3x^{2}+4x\right)+\left(18x+24\right)$$

Factor out x in the first and 6 in the second group.

$$x\left(3x+4\right)+6\left(3x+4\right)$$

Factor out common term 3x+4 by using distributive property.

$$\left(3x+4\right)\left(x+6\right)$$

Evaluate

$$\left(x+6\right)\left(3x+4\right)$$

Solution Steps

Combine 4x and 18x to get 22x.

$$3x^{2}+22x+24$$