Polynomials can be classified based on two primary characteristics: the number of terms they contain and their degree. According to the provided reference, polynomials should have a whole number as the degree.
Classification by Number of Terms
Polynomials are classified into three types based on the number of terms:
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Monomial: A polynomial with only one term.
- Example: 5x, 7, 3y2
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Binomial: A polynomial with two terms.
- Example: x + 2, 4y - 3, a2 + b2
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Trinomial: A polynomial with three terms.
- Example: x2 + 3x + 1, 2a - b + c, p3 + q + r
Classification by Degree
The degree of a polynomial is the highest power of the variable in the polynomial. Polynomials are classified into four types based on their degree:
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Zero Polynomial: A polynomial where all the coefficients are zero. The degree is undefined or sometimes defined as -1.
- Example: 0
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Linear Polynomial: A polynomial of degree 1.
- Example: x + 1, 2y - 5, 3z
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Quadratic Polynomial: A polynomial of degree 2.
- Example: x2 + 2x + 1, 3y2 - y + 4
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Cubic Polynomial: A polynomial of degree 3.
- Example: x3 + x2 + x + 1, 2y3 - 3y + 5
Here's a table summarizing the classifications:
| Classification Criteria | Type | Definition | Example(s) |
|---|---|---|---|
| By Number of Terms | Monomial | One term | 5x, 7, 3y2 |
| Binomial | Two terms | x + 2, 4y - 3, a2 + b2 | |
| Trinomial | Three terms | x2 + 3x + 1 | |
| By Degree | Zero Polynomial | All coefficients are zero | 0 |
| Linear Polynomial | Degree 1 | x + 1, 2y - 5 | |
| Quadratic Polynomial | Degree 2 | x2 + 2x + 1 | |
| Cubic Polynomial | Degree 3 | x3 + x2 + x + 1 |
It's important to remember that the degree of a polynomial must be a whole number.
