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polynomial operations

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
Feb 23rd, 2017
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