Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"
A polynomial can have:
constants (like 3, −20, or ½) variables (like x and y) exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed that can be combined using addition, subtraction, multiplication and division ...
... except ...
... not division by a variable (so something like 2/x is right out)
So:
A polynomial can have constants, variables and exponents, but never division by a variable.
Also they can have one or more terms, but not an infinite number of terms.
These are polynomials:
3x x − 2 −6y2 − ( 79 )x 3xyz + 3xy2z − 0.1xz − 200y + 0.5 512v5 + 99w5 5 (Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!)
These are not polynomials
3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...) 2/(x+2) is not, because dividing by a variable is not allowed 1/x is not either √x is not, because the exponent is "½" (see fractional exponents)
But these are allowed:
x/2 is allowed, because you can divide by a constant also 3x/8 for the same reason √2 is allowed, because it is a constant (= 1.4142...etc)
There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.
