Write in the form

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

Write

\dfrac{2x^{4}-3x^{3}+5x^{2}-4x+1}{x^{2}+1}

in the form

S(x)+\dfrac{R(x)}{x^{2}+1}

, where

\deg R<2

. Which of the following is correct? (a)

2x^{2}-3x-3+\dfrac{x-2}{x^{2}+1}

(b)

2x^{2}-3x-\dfrac{x+2}{x^{2}+1}

(c)

2x^{2}-3x+3-\dfrac{x+2}{x^{2}+1}

(d)

2x^{2}-3x+3+\dfrac{x+2}{x^{2}+1}