The classification of a polynomial is based on its degree, which is the highest power of the variable in the polynomial.
Polynomial Classification by Degree
Polynomials are categorized into different types based on their degree. Here's a breakdown:
| Degree | Classification | Example |
|---|---|---|
| 0 | Constant | 5 |
| 1 | Linear | 3x + 2 |
| 2 | Quadratic | 2x2 + x - 1 |
| 3 | Cubic | x3 - 4x2 + x - 6 |
| 4 | Quartic (or Biquadratic) | x4 + 3x2 + 2 |
| 5 | Quintic | x5 - 1 |
| 6 | Sextic (or Hexic) | x6 + 2x |
| n | nth-degree Polynomial | anxn + ... + a1x + a0 |
Explanation of Classifications:
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Constant: A polynomial with a degree of 0 has only a constant term (a number).
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Linear: A polynomial with a degree of 1 has the highest power of the variable as 1. Its graph is a straight line.
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Quadratic: A polynomial with a degree of 2 has the highest power of the variable as 2. Its graph is a parabola.
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Cubic: A polynomial with a degree of 3 has the highest power of the variable as 3.
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Quartic: A polynomial with a degree of 4 has the highest power of the variable as 4. If all terms have even degree, it can also be called biquadratic.
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Quintic: A polynomial with a degree of 5 has the highest power of the variable as 5.
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Sextic: A polynomial with a degree of 6 has the highest power of the variable as 6.
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nth-degree Polynomial: A polynomial with a degree of 'n' represents a generalized polynomial expression where 'n' is the highest power of the variable.
In summary, the degree of a polynomial determines its classification, influencing its properties and graph.
