Solve 36x^2+81x+4x+9

$$36 x ^ { 2 } + 81 x + 4 x + 9$$

Factor

$$\left(4x+9\right)\left(9x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$36x^{2}+85x+9$$

Factor the expression by grouping. First, the expression needs to be rewritten as 36x^{2}+ax+bx+9. To find a and b, set up a system to be solved.

$$a+b=85 ab=36\times 9=324$$

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 324.

$$1,324 2,162 3,108 4,81 6,54 9,36 12,27 18,18$$

Calculate the sum for each pair.

$$1+324=325 2+162=164 3+108=111 4+81=85 6+54=60 9+36=45 12+27=39 18+18=36$$

The solution is the pair that gives sum 85.

$$a=4 b=81$$

Rewrite 36x^{2}+85x+9 as \left(36x^{2}+4x\right)+\left(81x+9\right).

$$\left(36x^{2}+4x\right)+\left(81x+9\right)$$

Factor out 4x in the first and 9 in the second group.

$$4x\left(9x+1\right)+9\left(9x+1\right)$$

Factor out common term 9x+1 by using distributive property.

$$\left(9x+1\right)\left(4x+9\right)$$

Evaluate

$$\left(4x+9\right)\left(9x+1\right)$$

Solution Steps

Combine 81x and 4x to get 85x.

$$36x^{2}+85x+9$$