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x\left(3+2x-x^{2}\right)
Factor out x.
-x^{2}+2x+3
Consider 3+2x-x^{2}. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
a+b=2 ab=-3=-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=3 b=-1
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.
\left(-x^{2}+3x\right)+\left(-x+3\right)
Rewrite -x^{2}+2x+3 as \left(-x^{2}+3x\right)+\left(-x+3\right).
-x\left(x-3\right)-\left(x-3\right)
Factor out -x in the first and -1 in the second group.
\left(x-3\right)\left(-x-1\right)
Factor out common term x-3 by using distributive property.
x\left(x-3\right)\left(-x-1\right)
Rewrite the complete factored expression.