What is Irreducible (Prime) Polynomial ?

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What is Irreducible Polynomial ?

A polynomial that is not a fixed polynomial and cannot be written as the product of more than one polynomial is called Irreducible Polynomial or Prime Polynomial.

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What does Prime Polynomial mean ? Can you give me an example for Prime Polynomial ?

Polynomials that are not constant and cannot be written in the multiplication of more than one polynomial are called irreducible polynomial. P(x)=x2+x+1 is an example for prime polynomial.

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What does Irreducible Polynomial mean ?

Polynomials that are at least first order and cannot be factored into two polynomials are called irreducible polynomial.

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Can you factor a Prime Polynomial ?

It is not possible to factor a Prime Polynomial mathematically. These polynomials, like prime numbers, are in lowest common terms and you cannot factor them.

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Are all polynomials factorable ?

In algebra there are two types of polynomials. Reducible polynomials and Irreducible Polynomials (or Prime Polynomials). Irreducible polynomials can not be expressed as the multiplication of two seperate polynomials.

Can you give an example for Irreducible Polynomial ?

P(x)=x2+1 can not be factored. So it is an irreducible polynomial.

Can you give an example for Reducible Polynomial ?

P(x)=x2-1 is a reducible polynomial because x2-1=(x-1)(x+1).