is 2x^2+3/x a polynomial
Answers
Answer:
no sice power of x is not a whole number it is an Integer(negative)
While the other answers correctly state that f(x)=2x is not a polynomial, but an exponential function, they do not address why exponential functions are not polynomials.
A polynomial is of the form ∑Nn=0cnxn , where N is some positive integer, and cn∈F , where F is the field where you get your coefficients (most likely R or C ). As such, if given ∑Nn=0cnxn , we see that the N+1 st derivative is identically 0 . In other words, polynomials always differentiate to 0. On the other hand, if we have an exponential function ax , where a is a positive constant (which we assume is not 1 ), we can show that the n th derivative is ax(ln(a))n , which is never identically 0 . In other words, ax (where a≠1 ) never differentiates to 0 , and thus, exponential functions are not polynomials.