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Prove that if k is a eld and f (x), f (x) k [x] are relatively prime, then given b(x), b (x) k [x], there exisits c(x) k [x] with c b (f ) and c b (f...

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I'm trying to prove the Chinese Remainder Thm in k[x]. Please see the attachment for the full question.
Prove that if k is a field and f ( x ) ,f 0 ( x ) k [ x ] are relatively prime, then given b ( x ) ,b 0 ( x ) k [ x ], there exisits c ( x ) k [ x ] with c - b ( f ) and c - b 0 ( f 0 ) and if d(x) is another common solution, then c - d ( ff 0 ) 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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