Polynomials
A polynomial looks like this:
example of a polynomialthis one has 3 terms
Polynomialcomes frompoly-(meaning "many") and-nomial(in this case meaning "term") ... so it says "many terms"
A polynomial can have:
constants(like3,-20, or½)variables(likexandy)exponents(like the 2 in y
2), but only0, 1, 2, 3, ...etc are allowed
that can be combined usingaddition, subtraction, multiplication and division...
... except ...
...notdivision by a variable(so something like2/xis right out)
So:
A polynomial can have constants, variables and exponents,but never division by a variable.
Polynomial or Not?
Thesearepolynomials:
- 3x
- x - 2
- -6y2- (7/9)x
- 3xyz + 3xy2z - 0.1xz - 200y + 0.5
- 512v5+99w5
- 5
(Yes, even "5" is a polynomial,one term is allowed, and it can even be just a constant!)
And these arenotpolynomials
- 3xy-2is 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/xis not either
- √xis not, because the exponent is "½" (seefractional exponents)
Buttheseareallowed:
- x/2is allowed, because you can divide by a constant
- also3x/8for the same reason
- √2is allowed, because it is a constant (= 1.4142...etc)
Monomial, Binomial, Trinomial
There are special names for polynomials with 1, 2 or 3 terms:
