Is #f(x) (x^2 - 3x - 4)/(x^2 + 1)# a polynomial?

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Answer 1 · 2017-01-30T15:05:44

It is not a polynomial but an algebraic expression.

A polynomial is an expression consisting of

#-# variables (or indeterminates) and
#-# coefficients

and they involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents

It is of type #4x^2-7x+9# or could be some ting like

#xy^2-2x^2y^3+7y^2-x^3y#

but not #(x^2-3x-4)/(x^2+1)#, as this is actually a ratio of two polynomials

and is called an algebraic expression.