Question

what is ment by irredusabul factor​

Answer 1

Answer:

An irreducible quadratic factor is a quadratic factor in the factorization of a polynomial that cannot be factored any further over the real numbers. When it comes to the complete factorization of polynomials into irreducible factors, each factor corresponds to zeros of the polynomial.

Answer 2

Answer:

Irreducible factors are like prime numbers, but for polynomials. You can't write them as a product of lower order polynomials.

Example : x2−1 is not irreducible in Z[x] as it can be written as (x−1)(x+1)

x2+1 is irreducible in Z[x] as it cannot be written as a product of lower order polynomials.

However, x2+1 is reducible in Z2[x] as x2+1≡x2−1=(x+1)(x−1)

You can find the definition of irreducible here. An excellent theorem to check irreducibility in Z[x] is the Eisenstein's Criterion. There are other ways to check of course.