# polynomial operations

Anonymous
account_balance_wallet \$5

### Question Description

Does anybody know the rules for polynomials?

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

duingpung
School: Boston College

# 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:

flag Report DMCA
Review

Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors