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Prove that if k is a eld and f (x), g (x) k [x] are relatively prime, then k [x]/(f (x)g (x)) k [x]/(f (x)) k [x]/(g (x)) = 1


I'm trying to show a specific property using the chinese remainder thm. See attachment.

Prove that if k is a field and f ( x ) ,g ( x ) k [ x ] are relatively prime, then k [ x ] / ( f ( x ) g ( x )) = k [ x ] / ( f ( x )) × k [ x ] / ( g ( x )) 1
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Chinese Remainder Theorem.docx

Chinese Remainder Theorem
This theorem was first used by Chinese Mathematician Sun Tzu in third
century AD. This theorem states about simultaneous congruencies. It
says that suppose there are...

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