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x\left(x^{2}-6x+8\right)
Factor out x.
a+b=-6 ab=1\times 8=8
Consider x^{2}-6x+8. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+8. To find a and b, set up a system to be solved.
-1,-8 -2,-4
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 8.
-1-8=-9 -2-4=-6
Calculate the sum for each pair.
a=-4 b=-2
The solution is the pair that gives sum -6.
\left(x^{2}-4x\right)+\left(-2x+8\right)
Rewrite x^{2}-6x+8 as \left(x^{2}-4x\right)+\left(-2x+8\right).
x\left(x-4\right)-2\left(x-4\right)
Factor out x in the first and -2 in the second group.
\left(x-4\right)\left(x-2\right)
Factor out common term x-4 by using distributive property.
x\left(x-4\right)\left(x-2\right)
Rewrite the complete factored expression.