A polynomial looks like this:
|example of a polynomial
this one has 3 terms
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)|
A polynomial can have constants, variables and exponents,
but never division by a variable.
Polynomial or Not?
- x - 2
- -6y2 - (7/9)x
- 3xyz + 3xy2z - 0.1xz - 200y + 0.5
- 512v5+ 99w5
(Yes, even "5" is a polynomial, one term is allowed, and it can even be just a constant!)
And 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)
Monomial, Binomial, Trinomial
There are special names for polynomials with 1, 2 or 3 terms:
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