Factor
\left(x+1\right)\left(x+3\right)x^{2}
Evaluate
\left(x+1\right)\left(x+3\right)x^{2}
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x^{2}\left(x^{2}+4x+3\right)
Factor out x^{2}.
a+b=4 ab=1\times 3=3
Consider x^{2}+4x+3. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+3. To find a and b, set up a system to be solved.
a=1 b=3
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.
\left(x^{2}+x\right)+\left(3x+3\right)
Rewrite x^{2}+4x+3 as \left(x^{2}+x\right)+\left(3x+3\right).
x\left(x+1\right)+3\left(x+1\right)
Factor out x in the first and 3 in the second group.
\left(x+1\right)\left(x+3\right)
Factor out common term x+1 by using distributive property.
x^{2}\left(x+1\right)\left(x+3\right)
Rewrite the complete factored expression.
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Integration
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Limits
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