Solve 35x^2+21x+45x+27

$$35 x ^ { 2 } + 21 x + 45 x + 27$$

Factor

$$\left(5x+3\right)\left(7x+9\right)$$

Solution Steps

Multiply and combine like terms.

$$35x^{2}+66x+27$$

Factor the expression by grouping. First, the expression needs to be rewritten as 35x^{2}+ax+bx+27. To find a and b, set up a system to be solved.

$$a+b=66 ab=35\times 27=945$$

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 945.

$$1,945 3,315 5,189 7,135 9,105 15,63 21,45 27,35$$

Calculate the sum for each pair.

$$1+945=946 3+315=318 5+189=194 7+135=142 9+105=114 15+63=78 21+45=66 27+35=62$$

The solution is the pair that gives sum 66.

$$a=21 b=45$$

Rewrite 35x^{2}+66x+27 as \left(35x^{2}+21x\right)+\left(45x+27\right).

$$\left(35x^{2}+21x\right)+\left(45x+27\right)$$

Factor out 7x in the first and 9 in the second group.

$$7x\left(5x+3\right)+9\left(5x+3\right)$$

Factor out common term 5x+3 by using distributive property.

$$\left(5x+3\right)\left(7x+9\right)$$

Evaluate

$$\left(5x+3\right)\left(7x+9\right)$$

Solution Steps

Combine 21x and 45x to get 66x.

$$35x^{2}+66x+27$$