Factor
\left(x+3\right)\left(3x+1\right)
Evaluate
\left(x+3\right)\left(3x+1\right)
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3x^{2}+10x+3
Multiply and combine like terms.
a+b=10 ab=3\times 3=9
Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx+3. To find a and b, set up a system to be solved.
1,9 3,3
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 9.
1+9=10 3+3=6
Calculate the sum for each pair.
a=1 b=9
The solution is the pair that gives sum 10.
\left(3x^{2}+x\right)+\left(9x+3\right)
Rewrite 3x^{2}+10x+3 as \left(3x^{2}+x\right)+\left(9x+3\right).
x\left(3x+1\right)+3\left(3x+1\right)
Factor out x in the first and 3 in the second group.
\left(3x+1\right)\left(x+3\right)
Factor out common term 3x+1 by using distributive property.
3x^{2}+10x+3
Combine 9x and x to get 10x.
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