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

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 $4 {x}^{2} - 7 x + 9$ or could be some ting like

$x {y}^{2} - 2 {x}^{2} {y}^{3} + 7 {y}^{2} - {x}^{3} y$

but not $\frac{{x}^{2} - 3 x - 4}{{x}^{2} + 1}$, as this is actually a ratio of two polynomials

and is called an algebraic expression.