Question

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

Answer 1

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.