Answer
$(x-4)(x-2)$
Work Step by Step
The leading term's coefficient is $1$ so just look for factors of $8$ whose sum is equal to the middle term's coefficient which is $-6$. The factors are $-4$ and $-2$.
Rewrite the middle term ($-6x$) as $-4x-2x$ to obtain:
$x^2-6x+8=x^2-4x-2x+8$
Group the first two terms together and the last two terms together.
$=(x^2-4x)+(-2x+8)$
Factor out the GCF in each group.
$=x(x-4)-2(x-4)$
Factor out $(x-4)$.
$=(x-4)(x-2)$
Hence, the completely factored form of the given expression is $(x-4)(x-2)$.
