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