SOLUTION: 625x^4 − 16 factor polynomial completely. (5x-2)(5x+2)(25x-10i)(25x+10i) is this correct?

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Question 673372: 625x^4 − 16
factor polynomial completely.
(5x-2)(5x+2)(25x-10i)(25x+10i)
is this correct?

Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
625x^4 − 16
factor polynomial completely.
(5x-2)(5x+2)(25x-10i)(25x+10i)
is this correct?
==================
If you multiply the x terms, you get 15625x^4, so I'd say not.
= (5x-2)(5x+2)(25x + 4)
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Factor, unless spec'd otherwise, means integers, not complex numbers.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
625x^4 − 16
factor polynomial completely.
(5x-2)(5x+2)(25x-10i)(25x+10i)
is this correct?

This is a difference of two squares (DOTS) polynomial. As such, we get: %2825x%5E2+-+4%29%2825x%5E2+%2B+4%29). You did factor the 1st polynomial, 25x%5E2+-+4 further, but you now need to factor the sum of two-squares polynomial, (25x%5E2+%2B+4), further.

25x%5E2+%2B+4 = 25x%5E2+%2B+2%5E2 = (5x + 2i)(5x – 2i). This results in: highlight_green%28%285x+-+2%29%285x+%2B+2%29%285x+%2B+2i%29%285x+-+2i%29%29

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