Question

Factor x^2 - 2x + 3.

(x - 3)(x - 1)

(x + 3)(x + 1)

(x - 3)(x + 1)

Prime

@gowtham89

Answer 1

that is a prime, it can't be factored

Answer 2

the (-i x+sqrt(2)+i) (i x+sqrt(2)-i) would be the irreducible factors but factorization over finite fields would give
GF(2) | (x+1)^2
GF(3) | x (x+1)
GF(5) | x^2+3 x+3

Answer 3

Thank you