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x^{2}+9x+20
Multiply and combine like terms.
a+b=9 ab=1\times 20=20
Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+20. To find a and b, set up a system to be solved.
1,20 2,10 4,5
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=21 2+10=12 4+5=9
Calculate the sum for each pair.
a=4 b=5
The solution is the pair that gives sum 9.
\left(x^{2}+4x\right)+\left(5x+20\right)
Rewrite x^{2}+9x+20 as \left(x^{2}+4x\right)+\left(5x+20\right).
x\left(x+4\right)+5\left(x+4\right)
Factor out x in the first and 5 in the second group.
\left(x+4\right)\left(x+5\right)
Factor out common term x+4 by using distributive property.
x^{2}+9x+20
Combine 5x and 4x to get 9x.