/sci/ - Science & Math

i posted this in /sqt/, but didnt really get much of a response and i figure there are lots of people who know algebra things here

can someone explain what im misunderstanding about what's in the box:
i dont understand why [math] \deg g(X),\deg h(X)>0 [/math] should follow from [math] f(X) [/math] being reducible in [math] \mathbb{Z}[X] [/math].
for example, suppose [math] f(X)=4 [/math]. then [math] f(X) [/math] is reducible in [math] \mathbb{Z}[X] [/math] since 4 is not a unit, but [math] \deg 4=0 [/math]

one anon in /sqt/ thought maybe the lemma should also assume deg f>0, but idk.
i've put the definition of irreducible in the picture as someone mentioned it last time