Answer:
[tex](x+1)(x-1)(x-2)[/tex]
Step-by-step explanation:
[tex]x^3-2x^2-x+2[/tex]
Look at this as 2 separate expressions for now, being the first 2 terms and the last 2 terms:
[tex]\mbox{1. }x^3-2x^2\\\mbox{2. }-x+2[/tex]
Factor both of these individually, starting with the first one. The greatest common factor here is x², so factor that out:
[tex]\rightarrow x^3-2x^2\\\rightarrow x^2(x-2)[/tex]
Now the second equation. There isn't really a GCF here, but you still should factor out a -1 to get the x on its own.
[tex]\rightarrow -x+2\\\rightarrow -1(x-2)[/tex]
Together, that leaves you with this:
[tex]x^2(x-2)-1(x-2)[/tex]
This is actually another expression that can be factored. The GCF here is (x - 2):
[tex]\rightarrow x^2(x-2)-1(x-2)\\\rightarrow (x^2-1)(x-2)[/tex]
Finally, you can expand that (x² - 1) further using this rule:
[tex](x^2-y^2)=(x+y)(x-y)[/tex]
1 is equal to 1², so you can rewrite that term and then expand it with the rule above:
[tex]\rightarrow (x^2-1^2)(x-2)\\\rightarrow (x+1)(x-1)(x-2)[/tex]
