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

1 Answer
Jan 30, 2017

It is not a polynomial but an algebraic expression.

Explanation:

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.