S. D. V. Stephens

notes / Integrated Mathematics / chapter 8: College Algebra

27 Polynomial Functions

A polynomial function has the form written with the exponents descending from left to right.

  • Leading term: .
  • Constant term: .
  • Degree: (the largest exponent in the polynomial).
  • Domain: all real numbers.

Note. The exponents are all non-negative integers. Order by descending exponents when regarding polynomials.

Example 27.1. Find the degree, leading term and constant term of .

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Reorder: . Remember, this is . So the degree is , the leading term is , and the constant term is .

Example 27.2. Find the degree, leading term and constant term of .

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Reorder: . The degree is , the leading term is , and the constant term is .

Example 27.3. .

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Degree : this is a constant function, which is a polynomial of degree .

Example 27.4. .

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No degree.

Example 27.5. .

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Not a polynomial: the exponent is not an integer.

Example 27.6. .

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, so it is not a polynomial (negative exponent).

Example 27.7. .

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A polynomial, already in order :)

Example 27.8. .

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so it is not a polynomial.

Example 27.9. .

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, which is a polynomial.

Example 27.10. .

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, so it is not a polynomial.

Example 27.11. .

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which is a polynomial.