Mathxyz - upsc.xyz
0 votes
Let $F$ be a field and $F[X]$ denote the ring of polynomials over $F$ in a single variable $X$. For $f(X), g(X) \epsilon F[X]$ with $g(X) \neq 0$, show that there exist $q(X), r(X) \epsilon F[X]$ such that degree $(r(X)) < $ degree $(g(X))$ and $f(X) = q(X).g(X) + r(X)$.
asked Nov 25, 2017 by randomisation (1,920 points)  

Please log in or register to answer this question.

Welcome to MathXyz, where you can ask questions and receive answers from other members of the community. Please strictly ask questions from UPSC Mathematics syllabus.
37 questions
27 answers
2 comments
34 users