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Naming polynomials
There are some conventions for naming polynomials. Polynomials can be named by either their degrees or the numbers of terms, or both.
Naming polynomials by their degrees:
| Degree | Name | Example |
| 0 | constant | 5 |
| 1 | linear | 2x |
| 2 | quadratic | x2 + 3x + 2 |
| 3 | cubic | 2x3 - x2 + 3x +2 |
| 4 | quartic | x4 + 2x3 - x2 + 3x + 1 |
| 5 | quintic | x5 - 3x4 + x3 - 2x2 + x + 5 |
| 6 | sixth degree | 2x6 + 4x5 - x4 + 3x3 + 2x2 - x - 1 |
Naming polynomials by their numbers of terms:
| Number of terms | Name | Examples |
| 1 | monomial | 2 3x -3x4 |
| 2 | binomial | x + 3 x3 - x2 x + y |
| 3 | trinomial | x2 + 3x + 2 x4 - x2 + 1 x2 + 2xy + y2 |
| 4 | four terms polynomial | 2x3 - x2 + 3x +2 x5 - 2x2 + x + 5 x2 + 2xy + y2 + 1 |
Naming polynomials by both their degrees and numbers of terms:
| Name | monomial | binomial | trinomial |
| constant | constant monomial 3 |
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| linear | linear monomial 3x |
linear binomial 3x + 2, or 3x + 2y |
linear trinomial 3x + 2y + 1 |
| quadratic | quadratic monomial 3x2 |
quadratic binomial 3x2 + 2 |
quadratic trinomial 3x2 + x + 2 |
| cubic | cubic monomial 3x3 |
cubic binomial 3x3 + x |
cubic trinomial 3x3 + x + 1 |
| quartic | quartic monomial 3x4 |
quartic binomial 3x4 + 1 |
quartic trinomial 3x4 + 2x + 1 |
| quintic | quintic monomial 3x5 |
quintic binomial 3x5 + 2x3 |
quintic trinomial 3x5 + 2x3 + 1 |
More Examples
Name each of the following polynomials by its degree and number of terms:
1) x3 + 1
2) 2x + 3y
3) x3 + x2 +x +1
4) x5 - x4
Answers
1) cubic binomial
2) linear binomial
3) cubic polynomial with four terms
4) quintic binomial