Solve 2x^2+6x+5x+15

$$2 x ^ { 2 } + 6 x + 5 x + 15$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$2x^{2}+11x+15$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx+15. To find a and b, set up a system to be solved.

$$a+b=11 ab=2\times 15=30$$

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 30.

$$1,30 2,15 3,10 5,6$$

Calculate the sum for each pair.

$$1+30=31 2+15=17 3+10=13 5+6=11$$

The solution is the pair that gives sum 11.

$$a=5 b=6$$

Rewrite 2x^{2}+11x+15 as \left(2x^{2}+5x\right)+\left(6x+15\right).

$$\left(2x^{2}+5x\right)+\left(6x+15\right)$$

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

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

Factor out common term 2x+5 by using distributive property.

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

Evaluate

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

Solution Steps

Combine 6x and 5x to get 11x.

$$2x^{2}+11x+15$$