Polynomial functions are functions with exponents that are positive whole numbers. They can be expressed in standard or factored form and have different degrees corresponding to the highest power of x. Second-degree polynomials have the highest power of x being squared, like x^2 + 2x + 5. Their zeros and x-intercepts are opposites, except when there is a zero of multiplicity 2. Third-degree polynomials have the highest power being cubed, like x^3 + x - 3. Fourth-degree polynomials have the highest power being the fourth power, like x^4 - x^2 + 1.

1. Polynomial functionsBy: Kendra Coomes

2. What is a polynomial function?A polynomial function is a function with an exponent that is positive and has a whole number.Polynomials can be in standard form and factored form. They can also have different “degrees.”

3. What are degrees?Degrees are basically the function whenthe highest power of x is first in standard form. So if there was a x cubed and a 2x squared and a 5. The polynomial would be a third degree polynomial because the highest exponent was a 3.

4. Second-degree polynomialsExamples of a second-degree polynomial are:The reason these polynomials are second degree because the first x in both functions are squared.

5. Second-degree polynomials continued …The zero of the function and the x-intercept are always opposites.Example: if the zero of the function was 5 the x-intercept would be -5.The only time when both the zero of the function and the x-intercept could be the same is when there is a zero of multiplicity of 2.

6. Third-degree polynomialsExamples of third-degree polynomials are:These are both third-degree polynomials because the first x of each function is cubed.

7. Fourth-degree polynomialsThe following are examples of a fourth-degree polynomial:These are both fourth-degree polynomials because the first x of the function are both to the fourth power