Solve 5x^2+x+10x+2

$$5 x ^ { 2 } + x + 10 x + 2$$

Factor

$$\left(x+2\right)\left(5x+1\right)$$

Solution Steps

Multiply and combine like terms.

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

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

$$a+b=11 ab=5\times 2=10$$

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 10.

$$1,10 2,5$$

Calculate the sum for each pair.

$$1+10=11 2+5=7$$

The solution is the pair that gives sum 11.

$$a=1 b=10$$

Rewrite 5x^{2}+11x+2 as \left(5x^{2}+x\right)+\left(10x+2\right).

$$\left(5x^{2}+x\right)+\left(10x+2\right)$$

Factor out x in the first and 2 in the second group.

$$x\left(5x+1\right)+2\left(5x+1\right)$$

Factor out common term 5x+1 by using distributive property.

$$\left(5x+1\right)\left(x+2\right)$$

Evaluate

$$\left(x+2\right)\left(5x+1\right)$$

Solution Steps

Combine x and 10x to get 11x.

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