In other words, it is a polynomial of degree seven.

Hence is a polynomial of the same type as above.

The roots of this polynomial are 2, 1, and 11.

This happens with many, but not all, polynomials of degree 5 or higher.

There are three conditions, so p should be a polynomial of degree 2.

This can only be achieved if polynomials of degree 3 or higher are used.

Often simple models such as polynomials are used, at least initially.

These two polynomials are the same as those for the square knot.

In certain cases those polynomials could be defined over both a ground and an extension field.

The main difference lies in the fact that there is no natural total order on the polynomials.

They can also be polynomials - this is a rational function.

Many important knot polynomials can be defined in this way.

Further compare to the spread polynomials, in the section below.

The values of the polynomial are produced without ever having to multiply.

A second major way of classifying polynomials is by their degree.

They can sometimes be written in terms of Jacobi polynomials.

Moreover, each polynomial is raised to a power equal to its degree.

One of the simplest approaches is to fit a single polynomial in time.

The polynomials of the transfer function will all have real coefficients.

Most of those factors will be trivial, that is constant polynomials.

Each type has its uses; for more information see the article on matching polynomials.

The derivatives of the polynomials can be less than straightforward.

The set of binary polynomials is treated as a ring.

We need three values to uniquely fit a second degree polynomial.

It was years before I learned to communicate with other people without using polynomials."

Using multinomial regression on the sales data however will not tell us what we want to know.

Various methods may be used to simulate a multinomial distribution.

In practice the multinomial coefficient is usually removed from the calculation.

In the two cases, the result is a multinomial distribution with k categories without any correlation.

Furthermore, each topic defines a multinomial distribution over a set of terms.

This is the origin of the name "multinomial distribution".

All of the multinomial coefficients for which the following holds true:

Draw random samples of size 230 and 400 from the two multinomial populations defined above.

Models used in binomial regression can often be extended to multinomial data.

An introduction to the imprecise Dirichlet model for multinomial data.

However, conflating the categorical and multinomial distributions can lead to problems.

Then we get the following test statistic for negative multinomial distributed data:

This provides a quick way to generate a lookup table for multinomial coefficients.

Multinomial choice models can further be classified according to the model specification:

Their conditional distributions are assumed to be binomial or multinomial.

"Inferences from multinomial data: learning about a bag of marbles (with discussion)".

An example of the multivariate case is the multinomial distribution with known number of trials.

This leads to the Bag of words model, and turns out to generate a multinomial distribution over words.

Turing at first modeled the frequencies as a multinomial distribution, but found it inaccurate.

The multinomial unigram language model is commonly used to achieve this.

It connects the categorical distribution with the related multinomial distribution.

A single vector-valued variable , distributed according to a multinomial distribution.

In this model, the multinomial distributions and are generated from and , respectively.

For categorical variables with more than two values there is the multinomial logit.

Suppose is generalized Dirichlet, and that is multinomial with trials (here ).

For a basis-independent definition of 'polynomial' nothing is lost by referring to the symmetric powers of the given linear representation of Γ.

Kett petitioned King Edward VI of England with a large number of demands: The 'polynomial remainder theorem' in algebra is an application of polynomial long division.

To say that a finitely generated group has 'polynomial growth' means the number of elements of length (relative to a symmetric generating set) at most 'n' is bounded above by a polynomial function 'p'('n').