Polynomials are some of our favorite functions.

The functions you are most familiar with are probably polynomial functions.

1 What are polynomial functions?

Which of the following are polynomial functions?

The phrase above “in the variable ” can actually change.

is a polynomial in , and

is a polynomial in .

2 What can the graphs look like?

Fun fact:

Remember, a root is where a polynomial is zero. The theorem above is a deep fact of mathematics. The great mathematician Gauss proved the theorem in 1799 for his doctoral thesis.

The upshot as far as we are concerned is that when we plot a polynomial of degree , its graph will cross the -axis at most times.

2025-01-06 19:59:23