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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A non-constant polynomial, $P(x),$ is said to be an irreducible polynomial or prime polynomial over a set of numbers, if it cannot be factored into the product of two non-constant polynomials over the **same** set of numbers.

All polynomials of the form $P(x)=ax+b,$ where $a =0,$ are prime polynomials.

Over the set of the complex numbers, only the linear polynomials are prime. This can be proven by using the Fundamental Theorem of Algebra.