SOLUTION: I need help with the following problem please, including the steps to get to the answer if needed... thanks!! Factor the polynomial {{{s^2+25}}}. If the polynomial cannot be fac

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with the following problem please, including the steps to get to the answer if needed... thanks!! Factor the polynomial {{{s^2+25}}}. If the polynomial cannot be fac      Log On


   

Question 273699: I need help with the following problem please, including the steps to get to the answer if needed... thanks!!
Factor the polynomial s%5E2%2B25. If the polynomial cannot be factored, write PRIME.
Found 3 solutions by jim_thompson5910, stanbon, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Ask yourself the following: "Are there two whole numbers in which multiply to 25 AND add to 0 (the middle coefficient is 0 since the second term is 0s)?"


Since there aren't any numbers which satisfy the above, this means that we cannot factor s%5E2%2B25. So the polynomial is prime.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the polynomial s^2+25
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It is PRIME in the Real Number System.
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In the COMPLEX Number System it factors
as (s+5i)(s-5i) where i is the sqrt(-1).
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Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


In general, is not factorable over the reals, and I think that is what you mean here. Therefore your answer is PRIME.

However, IS factorable over the complex numbers.



Where is the imaginary number defined by

John