SOLUTION: I need to factor X^4 - 256 using complex numbers. At least that is what the instructor said. Please help.

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Question 17315: I need to factor X^4 - 256 using complex numbers. At least that is what the instructor said. Please help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to recognise the expression x%5E4+-+256 as the difference of two squares:
x%5E4+-+256+=+%28x%5E2%29%5E2+-+16%5E2
The difference of two squares is factored as:
A%5E2+-+B%5E2+=+%28A+%2B+B%29%28A+-+B%29
%28x%5E2%29%5E2+-+16%5E2+=+%28x%5E2+%2B+16%29%28x%5E2+-+16%29 Now you have both the sum of two squares and the difference of two squares.
The difference of two squares is factored as:
x%5E2+-+16+=+%28x+%2B+4%29%28x+-+4%29
The sum of two squares is factored as:
A%5E2+%2B+B%5E2+=+%28A+%2B+Bi%29%28A+-+Bi%29
So, x%5E2+%2B+16+=+%28x+%2B+4i%29%28x+-+4i%29
x%5E4+-+256+=+%28x+%2B+4%29%28x+-+4%29%28x+%2B+4i%29%28x+-+4i%29