For the rational expression

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

For the rational expression x3+2x2+1x2+1\dfrac{x^{3}+2x^{2}+1}{x^{2}+1}, the expression can be written in the form Q(x)+Ax+Bx2+1Q(x)+\dfrac{Ax+B}{x^{2}+1}. Identify the greatest possible degree of the polynomial Q(x)Q(x) and briefly explain—using one sentence—why the numerator Ax+BAx+B cannot have degree 2 or higher.

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