SOLUTION: x^12 - 1 Factor.

Question 8167: x^12 - 1
Factor.
Found 2 solutions by longjonsilver, Earlsdon:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
this is a difference of 2 squares, if written as ...so we can write this as

jon.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Ok,this gets a little messy, so please bear with me.
Factor: Start with the difference of two squares.
NB:
Take the first factor: and note that it is also the difference of two squares.

Notice here that the 1st factor is the difference of two cubes and that the second factor is the sum of two cubes. These can be factored using the formulas:
and;

So, we have:
and;

Now, going back to the first line, let's look at the 2nd factor: and factor this:

Now we can put it all together:
Whew!
You can verify this by multiplying all of these factors to see that you get I'll leave this as an exercise for the student.
A final note:
I have left the factor in its unfactored form, not because it can't be factored, but because I don't know whether or not you have covered complex numbers yet. But, in case you have, here's how you would factor
where:
Using FOIL to check:
NB: = -1
=

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