We know that [tex]8=2\cdot4[/tex], and that [tex]-(2+4)=-6[/tex]. Then if we write
[tex]x^2-6x+8=x^2-4x-2x+8=(x^2-4x)+(-2x+8)[/tex]
then pull out common factors from the grouped terms to get
[tex]x(x-4)-2(x-4)[/tex]
we can apply the distributive property to end up with the factorization
[tex](x-2)(x-4)[/tex]
