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anonymous
 4 years ago
how to factor this binomial?
25x^2+1
anonymous
 4 years ago
how to factor this binomial? 25x^2+1

This Question is Closed

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.2\[a^2+b^2=(a+ib)(aib)\]

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2That is the sum of two squares and it is prime within the set of real numbers.

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2What class are you taking?

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2So have you had imaginary numbers yet?

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2Then put down that this binomial cannot be factored and is prime.

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2If it were the difference of two squares, it would be factorable but since it is the sum of two squares, it is prime.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so what's the difference of sum/diff of squares?

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2x^2 is a square 16 is a square x^+16 is the sum of two squares and cannot be factored x^216 is the difference of two squares and can be factored.

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2Sum means add. Difference means subtract.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so whenever there is a  sign it can be factored and when + is prime?

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2Yes. If those signs join two squares.

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.2Mertsj: why do say this must be prime? (e.g. when x=1, we get \(25x^2+1=26\) which is not a prime number.

Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.2Prime means has no factors except itself and 1

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.2so mean the "expression" is prime rather than the number that it produces?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.2ok  thx for clarifying

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.0x^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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