If all of its terms are of the form ax^b where a is any constant and b is a non-negative integer then it is a polynomial. If not, it is not.
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Do the division, and see if there is a remainder.
The degree of a polynomial is the highest power that appears in the polynomial. For more than one variable, you must add the powers for each variable, for example, a3b2 is of degree 3 + 2 = 5.
It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial).
Polynomial vs non polynomial time complexity
No.