What is the difference between polynomial and non polynomial?

Answer 1

non-polynomials are a lot more complicated than polynomials

Answer 2

A polynomial is a sum of monomials - and each monomial may only contain non-negative integer powers of the variables involved. If any other operation is involved (for example, a negative or fractional exponent; equivalent to a variable in the denominator, or a root), you have a non-polynomial.

Answer 3

A polynomial consists only of powers of the variables - ie the variables multiplied by themselves or one another. A non polynomial can include any other function such as trigonometric, exponential, logarithmic etc.

Answer 4

A polynomial is a function comprising of a finite number of non-negative integer powers of one variable. Thus given a variable x, a polynomial in x is any function of the type

a0 + a1x + a2x2 + ... + anxn for some finite number n, where a0, ... an are constants.

A non-polynomial is any other function of one, or more, variables. These could be trigonometric, exponential, logarithmic or involve fractional or negative powers.

Answer 5

"Non-polynomials", having none of the properties or characteristics of polynomials,

or even having some but not all of those features, have no legitimate claim to the

descriptive title "polynomial".

In contrast, "polynomials" are observed upon the closest examination to match the

formal definition of that class of expressions in every detail, by virtue of which they

are entitled to that coveted appellation, along with all of the rights and privileges

to which its holders are rightful heirs.

Answer 6

A polynomial is a sum of monomials - and each monomial may only contain non-negative integer powers of the variables involved. If any other operation is involved (for example, a negative or fractional exponent; equivalent to a variable in the denominator, or a root), you have a non-polynomial.