Question 973472: Could you help me factor the polynomial t2 + 4z2 and explain how it's done? Found 2 solutions by stanbon, Alan3354:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! factor the polynomial t2 + 4z2
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You have to know the factors of the sam of 2 squares::
x^2 + y^2 = (x+yi)(x-yi)
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Your Problem::
t^2 + 4z^2 = (t+2zi)(t-2zi)
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Cheers,
Stan H.
You can put this solution on YOUR website! Could you help me factor the polynomial t2 + 4z2 and explain how it's done?
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That's not factorable, it's prime.
Most polynomials are prime, ie, they cannot be factored using integers.
eg, x^2 + 4, x^2 + 5, etc. x^2 + k if k is positive is prime.
Saying x^2 + 5 = (x + isqrt(5))*(x - isqrt(5)) implies that there are no prime polynomials.
PS
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A sum of 2 squares cannot be factored in general.
A difference of 2 squares can be.
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