polynomial example

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)

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.

Polynomial or Not?

polynomial

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)

Monomial, Binomial, Trinomial

There are SPECIAL NAMES for polynomials with 1, 2 or 3 terms:

monomial, binomial, trinomial