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.
Polynomial or Not?
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
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)
sources
https://www.mathsisfun.com/algebra/polynomials.html