To know which of the following expressions are polynomials, let us look at the definition of a polynomial:
Polynomial is derived from poly- (which means "many") and -nomial (meaning "term"), so it says "many terms".
For an instance: [tex]2x^2y+2y^2[/tex] is a polynomial, but [tex]4xy^2[/tex] is not a polynomial because it contains single term only.
We must keep in mind that in polynomial it can have variables, constants, and exponents but it can never have division by a variable.
Now lets, look at the
[tex]30y^2[/tex] since it has got one term it can not be a polynomial.
[tex]30y^2+x[/tex]: it has got more than one term therefore, it is a polynomial.
[tex]30y^2x[/tex]: again it has got just one term so it is not a polynomial.
[tex]30y^2+x^{12}[/tex]: Since it has got more than one term, so again it is a polynomial.
