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
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Question 273699: I need help with the following problem please, including the steps to get to the answer if needed... thanks!!
Factor the polynomial . If the polynomial cannot be factored, write PRIME.
Found 3 solutions by jim_thompson5910, stanbon, solver91311:
Answer by jim_thompson5910(35256) (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 )?"
Since there aren't any numbers which satisfy the above, this means that we cannot factor . So the polynomial is prime.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Factor the polynomial s^2+25
----
It is PRIME in the Real Number System.
---
In the COMPLEX Number System it factors
as (s+5i)(s-5i) where i is the sqrt(-1).
=====================
Cheers,
Stan H.
Answer by solver91311(24713) (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.
\left(s\ +\ 5i\right))
Where 
is the imaginary number defined by 
John
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