On the previous page, you explored the key components that define a polynomial function. This unit covers only polynomials of degree ≤ 3; so, it is useful to write the definition explicitly for each of these functions. This is called standard form of the polynomial.
| constant function: |
ƒ(x) = a, a ≠0 |
degree = 0 |
| linear function: |
ƒ(x) = ax + b, a ≠0 |
degree = 1 |
| quadratic function: |
ƒ(x) = ax2 + bx + c, a ≠0 |
degree = 2 |
| cubic function: |
ƒ(x) = ax3 + bx2 + cx + d, a ≠0 |
degree = 3 |
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Which of the following are polynomial functions? Explain your reasoning.
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- ƒ(x) is a polynomial function in standard form. The degree is 3, a whole number. The coefficients are 4 and −5 and the constant term is
 . These are all real numbers.
- g(x) is not a polynomial function. Because of the exponent −1, the expression cannot be written in standard form.
- h(x) is not a polynomial function. Because of the square root, the expression cannot be written in standard form.
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k(x) is a polynomial function. In standard form, k(x) = −2x2 + 15x. The degree is 2, a whole number. The coefficients are 15 and −2 and the constant term is 0. These are all real numbers.
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