Solve 6x^2+11x+3+2

$$6 x ^ { 2 } + 11 x + 3 + 2$$

Factor

$$\left(x+1\right)\left(6x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{2}+11x+5$$

Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx+5. To find a and b, set up a system to be solved.

$$a+b=11 ab=6\times 5=30$$

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

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

Factor out x in 6x^{2}+5x.

$$x\left(6x+5\right)+6x+5$$

Factor out common term 6x+5 by using distributive property.

$$\left(6x+5\right)\left(x+1\right)$$

Evaluate

$$\left(x+1\right)\left(6x+5\right)$$

Solution Steps

Add 3 and 2 to get 5.

$$6x^{2}+11x+5$$