Need help with factoring this problem. Just want to make sure I followed the right steps.
X^3-2X^2-X+2
there are four terms so i used grouping method
X^2(X-2)(-1)(X-2)
(X-2) (X^2-1)
(X-2) (X-1) (X+1)
Correct?
correct~ :)
Yes, your steps for factoring the expression X^3-2X^2-X+2 using the grouping method are correct. However, there is a small mistake in your final factored expression.
Let me explain the steps in more detail:
1. Start by grouping the terms in pairs. In this case, we can group the first two terms (X^3-2X^2) and the last two terms (-X+2).
2. Factor out the greatest common factor from each pair separately. From the first pair, you can factor out X^2: X^2(X-2). From the second pair, you can factor out -1: -1(X-2).
3. Now, notice that both X^2(X-2) and -1(X-2) have a common factor of (X-2). So you can factor out this common binomial term: (X-2)(X^2-1).
4. Finally, notice that X^2-1 can be further factored using the difference of squares formula: X^2-1 = (X+1)(X-1).
Putting it all together, the factored expression is (X-2)(X+1)(X-1). So the correct factored expression for X^3-2X^2-X+2 is (X-2)(X+1)(X-1).
I hope this explanation helps clarify the process for factoring the given expression.