a.) Let R be an integral domain and f(x), g(x) are elements of R[x]. Prove that deg(f(x)g(x))=deg(f(x))+deg(g(x)). b.) Is part (a) true if R is not an integral domain?
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Originally Posted by Slazenger3 a.) Let R be an integral domain and f(x), g(x) are elements of R[x]. Prove that deg(f(x)g(x))=deg(f(x))+deg(g(x)). b.) Is part (a) true if R is not an integral domain? a) let then the leading term of is and because and is an integral domain. b) no! a counter-example:
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