A) If \[g(x)(\ne 0)\] and \[f(x)\] are two polynomials\[\in F(x)\], then there exists unique polynomials q\[q(x)\]and\[r(x)\in F(x)\]such that\[f(x)=g(x)q(x)+r(x)\], where deg.\[\deg .r(x),\deg .g(x)\].
B) If\[g(x)(\ne 0)\]and\[f(x)\]are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and\[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\]where deg. \[r(x)<\]: deg. \[g(x)\].
C) If \[g(x)(\ne ,0)\] and\[f(x)\] are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and \[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\], where either \[r(x)=0\] or deg. \[r(x)<\]deg. \[g(x)\]
D) If \[g(x)(\ne ,0)\] and\[f(x)\] are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and \[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\], where either \[r(x)=0\] or deg. \[r(x)<\]deg. \[g(x)\]
Correct Answer: D
Solution :
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