Sorry this is more of a language issue. If $f(x) \in F[x]$, and if $f$ is not irreducible, does it mean it is reducible? Since this is just a language question, I am allowing $F$ to be a commutative ring with unity instead of a field like usual.
Not irreducible = reducible.
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abstract-algebra
terminology
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0@angryavian, thanks – 2017-01-30
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0Units in $F^{\times}$ are probably not called reducible – 2017-01-30
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0@angryavian Wikipedia forgot to consider zero and units (or constants). Wikipedia is far from authoritative. – 2017-01-30