I don't understand the polynomials

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)