How different the polynomials and non polynomials?

Answer 1

Well, "non-polynomial" can be just about anything; presumably you mean a non-polynomial FUNCTION, but there are lots of different types of functions. Polynomials, among other things, have the following properties - assuming you have an expression of the type y = P(x):* The polynomial is defined for any value of "x".

* The polynomial makes is continuous; i.e., it doesn't make sudden "jumps".

* Similarly, the first derivative, the second derivative, etc., are continuous.

A non-polynomial function may not have all of these properties; for example:

* A rational function is not defined at any point where the denominator is zero.

* The square root function is not defined for negative values.

* The first derivative (i.e., the slope) of the absolute value function makes a sudden jump at x = 0.

* The function that takes the integer part of any real number makes sudden jumps at all integers.

Answer 2

A polynomial in x is an expression of the form anxn + an-1xn-1 + ... + a2x2 + a1x + a0 where an , an-1 , ... a2 , a1 , a0 , x is a variable and the powers of x are all positive integers. A non-polynomial is any other function of the variable x.