Definition Punctuation

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Nathan Nguyen
2025-02-09 22:37:28 -06:00
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@@ -46,7 +46,7 @@ where either $\deg r(x) < \deg g(x)$ or $r(x)$ is the zero polynomial.
## Section 17.3 Irreducible Polynomials
**Definition** A non-constant polynomial $f(x) \ in F[x]$ is *irreducible* over a field $F$ if it cannot be expressed as the product of two non-identity polynomials $g(x)$ and $h(x)$ in $F[x]$, with the degree of both polynomials strictly less than the degree of $f(x)$.
**Definition**. A non-constant polynomial $f(x) \ in F[x]$ is *irreducible* over a field $F$ if it cannot be expressed as the product of two non-identity polynomials $g(x)$ and $h(x)$ in $F[x]$, with the degree of both polynomials strictly less than the degree of $f(x)$.
**Lemma**. Let $p(x) \in \mathbb{Q}[x]$. Then, with $r, s \in \mathbb{Z}, a(x) \in \mathbb{N}[x]$, we can write $p(x) = \frac{r}{s} a(x)$.