If quadratic or cubic polynomial $f$ has no roots, then $f$ is irreducible.
Solution 1:
Suppose that $f$ is reducible, $f=gh$ where $deg(f)+deg(g)=3$ and $deg(f),deg(g)>0$ this implies that $deg(f)=1$ or $deg(g)=1$ and $f$ has a root.
If quadratic or cubic polynomial $f$ has no roots, then $f$ is irreducible.
Solution 1:
Suppose that $f$ is reducible, $f=gh$ where $deg(f)+deg(g)=3$ and $deg(f),deg(g)>0$ this implies that $deg(f)=1$ or $deg(g)=1$ and $f$ has a root.