How can you tell if something is or is not a polynomial?

Question

amistre64 · Answer

a poly only has positive integer powers

anonymous · Answer

a polynomial consists of or characterized by two or more names or terms.

amistre64 · Answer

no, thats not the definition of a polynomial

amistre64 · Answer

f(x) = 3  is a polynomial

anonymous · Answer

No, 3x is a polynomial.

amistre64 · Answer

$$P_n(x)=c_0+c_1x+c_2x^2+...+c_nx^n$$

adilalvi · Answer

A polynomial is a monomial or the sum or difference of monomials. Each monomial is called a term of the poynomial

amistre64 · Answer

f(x) = 3x is a polynomial yes ... but even that only has 1 term

amistre64 · Answer

your def of "a polynomial consists of or characterized by two or more names or terms" excludes f(x) = 3x

amistre64 · Answer

but then you say that f(x) = 3x IS a poly :)

e.mccormick · Answer

$f(x) = 3x\implies f(x)=0x^2+3x\therefore $ $f(x) = 3x$ is a poly.

e.mccormick · Answer

The big key is the exponents are non-negative integers.  So $x^{\tfrac{2}{3}}$ is not a poly and $x^{-2}$ is not a poly.

amistre64 · Answer

x^0 is frowned on by many texts since it leads to the 0^0 situation

e.mccormick · Answer

Understandable!  That leads to some hard to define areas.... and  $\tfrac{0^0}{0^0}$ would really be confusing to try and guess the meaning of.

amistre64 · Answer

:)  indeed