Factor
\frac{\left(1-x\right)\left(x+3\right)}{3}
Evaluate
\frac{\left(1-x\right)\left(x+3\right)}{3}
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\frac{-x^{2}-2x+3}{3}
Factor out \frac{1}{3}.
a+b=-2 ab=-3=-3
Consider -x^{2}-2x+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 negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
\left(-x^{2}+x\right)+\left(-3x+3\right)
Rewrite -x^{2}-2x+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.
\frac{\left(-x+1\right)\left(x+3\right)}{3}
Rewrite the complete factored expression.
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Simultaneous equation
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Integration
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Limits
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