Solve 2+4j+5j+10j^2

$$2 + 4 j + 5 j + 10 j ^ { 2 }$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$10j^{2}+9j+2$$

Factor the expression by grouping. First, the expression needs to be rewritten as 10j^{2}+aj+bj+2. To find a and b, set up a system to be solved.

$$a+b=9 ab=10\times 2=20$$

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 20.

$$1,20 2,10 4,5$$

Calculate the sum for each pair.

$$1+20=21 2+10=12 4+5=9$$

The solution is the pair that gives sum 9.

$$a=4 b=5$$

Rewrite 10j^{2}+9j+2 as \left(10j^{2}+4j\right)+\left(5j+2\right).

$$\left(10j^{2}+4j\right)+\left(5j+2\right)$$

Factor out 2j in 10j^{2}+4j.

$$2j\left(5j+2\right)+5j+2$$

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

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

Evaluate

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

Solution Steps

Combine 4j and 5j to get 9j.

$$2+9j+10j^{2}$$