The standard form of a polynomial function arranges the terms by degree in descending numerical order.
A polynomial function P(x) in standard form is
where n is a nonnegative integer and
You can classify a polynomial by its degree or by its number of terms. Polynomials of degrees zero through five have specific names, as shown in this table.
Degree | Name Using Degree | Polynomial Example | Number of Terms | Name Using Number of Terms |
---|---|---|---|---|
0 | constant | 5 | 1 | monomial |
1 | linear |
|
2 | binomial |
2 | quadratic |
|
1 | monomial |
3 | cubic |
|
3 | trinomial |
4 | quartic |
|
2 | binomial |
5 | quintic |
|
4 | polynomial of 4 terms |
Write each polynomial in standard form. What is the classification of each polynomial by degree? by number of terms?
How do you write a polynomial in standard form?
Combine like terms if possible. Then, write the terms with their degrees in descending order.
The polynomial has degree 2 and 3 terms. It is a quadratic trinomial.
The polynomial has degree 4 and 4 terms. It is a quartic polynomial of 4 terms.
Write each polynomial in standard form. What is the classification of each by degree? by number of terms?