how to factor this binomial? 25x^2+1

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how to factor this binomial? 25x^2+1

Mathematics
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(-i+5 x) (i+5 x)
\[a^2+b^2=(a+ib)(a-ib)\]
That is the sum of two squares and it is prime within the set of real numbers.

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Other answers:

What class are you taking?
algebra...
So have you had imaginary numbers yet?
no
Then put down that this binomial cannot be factored and is prime.
If it were the difference of two squares, it would be factorable but since it is the sum of two squares, it is prime.
so what's the difference of sum/diff of squares?
x^2 is a square 16 is a square x^+16 is the sum of two squares and cannot be factored x^2-16 is the difference of two squares and can be factored.
Sum means add. Difference means subtract.
so whenever there is a - sign it can be factored and when + is prime?
Yes. If those signs join two squares.
Mertsj: why do say this must be prime? (e.g. when x=1, we get \(25x^2+1=26\) which is not a prime number.
Prime means has no factors except itself and 1
so mean the "expression" is prime rather than the number that it produces?
Yes
ok - thx for clarifying
5 is prime
x^2+4 is prime
yw
got you!!!
Good
x^2 + 4 is a prime expression over the set of Reals but is not prime over the set of Complex numbers.

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