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# Definitions

A monomial, the simplest kind of polynomial, is made up by multiplying variables, possibly with exponents, by numbers. For example,

x3x2y5z473x2y5x5

are all monomials. The fact that the first one has only one variable, the third has no variables at all and the fourth can be simplified by combining the x terms doesn't matter. All the expressions have nothing but variables/numbers being multiplied together.

These expressions, on the other hand, aren't monomials

 x2 + y addition isn't allowed x2 / y division isn't allowed x1/2 fractional exponents aren't allowed x-1 negative exponents aren't allowed

A polynomial, on the otherhand, is just the sum (or difference) of a bunch of monomials. For example,

x + 73x2y5z4 + 3y2z3-7 + x + y

The number of variables doesn't matter and their arrangement doesn't matter. Other than that, all the rules for monomials still apply. You can't divide, you can't have negative exponents and you can't have fractional exponents. You also can't have any "functions" other than exponents. For example, log(x) + 1 isn't a polynomial because of the logarithm function.