Solve 2j^2+2j+3j+3

$$2 j ^ { 2 } + 2 j + 3 j + 3$$

Factor

$$\left(j+1\right)\left(2j+3\right)$$

Solution Steps

Multiply and combine like terms.

$$2j^{2}+5j+3$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2j^{2}+aj+bj+3. To find a and b, set up a system to be solved.

$$a+b=5 ab=2\times 3=6$$

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 6.

$$1,6 2,3$$

Calculate the sum for each pair.

$$1+6=7 2+3=5$$

The solution is the pair that gives sum 5.

$$a=2 b=3$$

Rewrite 2j^{2}+5j+3 as \left(2j^{2}+2j\right)+\left(3j+3\right).

$$\left(2j^{2}+2j\right)+\left(3j+3\right)$$

Factor out 2j in the first and 3 in the second group.

$$2j\left(j+1\right)+3\left(j+1\right)$$

Factor out common term j+1 by using distributive property.

$$\left(j+1\right)\left(2j+3\right)$$

Evaluate

$$\left(j+1\right)\left(2j+3\right)$$

Solution Steps

Combine 2j and 3j to get 5j.

$$2j^{2}+5j+3$$