How to tell if a polynomial is prime?
Understand the Problem
The question is asking how to determine whether a given polynomial is irreducible or prime, meaning it cannot be factored into simpler polynomials over the same field or ring.
Answer
If it cannot be factored into lower degree polynomials with integer coefficients, it is prime.
If the polynomial cannot be factored into lower degree polynomials with integer coefficients, it is prime.
Answer for screen readers
If the polynomial cannot be factored into lower degree polynomials with integer coefficients, it is prime.
More Information
A prime or irreducible polynomial is akin to a prime number in integer arithmetic. It cannot be factored further over its coefficient field.
Tips
Be sure to explore different methods such as factoring, polynomial division, and using the quadratic formula as appropriate for the degree of the polynomial.
Sources
- Factoring Polynomials - sparknotes.com
- Irreducible Polynomial - mathworld.wolfram.com
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