The expression Q(x)=(x^ 2 -3x+1)+(4x^ -1 +5)+3 x is under consideration.

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

The expression

Q(x)=(x^{2}-3x+1)+(4x^{-1}+5)+3\sqrt{x}

is under consideration. (i) Identify and list the term(s) that prevent

Q(x)

from being a polynomial in

x

. Explain why each listed term is not permitted in a polynomial. (ii) By omitting only the non-polynomial term(s), write the remaining expression

R(x)

and arrange it in descending powers of

x

. (iii) Verify that

R(x)

is a polynomial and state its degree.