SOLUTION: factor completely 3(x-2)^2-3(x-2)-6

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Question 49573: factor completely
3(x-2)^2-3(x-2)-6
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely:
3%28x-2%29%5E2+-+3%28x-2%29+-+6
You can factor this expression in a couple of ways.
1) 3%28x-2%29%5E2-3%28x-2%29-6 Factor a 3.
3%28%28x-2%29%5E2-%28x-2%29-2%29 Expand the parentheses.
3%28%28x%5E2-4x%2B4%29-%28x-2%29-2%29 Simplify.
3%28x%5E2-5x%2B4%29 Finally, factor the parentheses.
3%28x-1%29%28x-4%29
The other way:
2) 3%28x-2%29%5E2-3%28x-2%29-6 Again, factor the 3.
3%28%28x-2%29%5E2-%28x-2%29-2%29 Now substitute a for (x-2).
3%28a%5E2-a-2%29 Factor the parentheses.
3%28a-2%29%28a%2B1%29 Now replace a with (x-2).
3%28x-2-2%29%28x-2%2B1%29 Simplify this.
3%28x-4%29%28x-1%29 Compare this answer with 3%28x-1%29%28x-4%29 above!