# Polynomials in Integers is Unique Factorization Domain

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## Theorem

Let $\Z \sqbrk X$ be the ring of polynomials in $X$ over $\Z$.

Then $\Z \sqbrk X$ is a unique factorization domain.

## Proof

We have that Integers form Unique Factorization Domain.

The result follows from Gauss's Lemma on Unique Factorization Domains.

$\blacksquare$