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##### polynomial operations

label Algebra
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Does anybody know the rules for polynomials?

like addition - you add such and such and keep exponents.. stuff like that

Aug 13th, 2014

# Polynomials

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)

So:

A polynomial can have constants, variables and exponents,
but never division by a variable.

## Polynomial or Not?

These arepolynomials:

• 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 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:

Aug 13th, 2014

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Aug 13th, 2014
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Aug 13th, 2014
Aug 16th, 2017
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