# Polynomial expressions, equations, and functions

Contents

Learn how to manipulate polynomials in order to prove identities and find the zeros of those polynomials. Use this knowledge to solve polynomial equations and graph polynomial functions. Learn about symmetry of functions.

Learn how to expand powers of binomial expressions (which are polynomial expressions with exactly two terms). This is done using the binomial theorem!

Now that you know how to use the binomial theorem in order to expand powers of binomial expressions, let's gain further insight into why this actually works!

Learn how to factor quadratic polynomials of the form ax^2+bx+c as the product of two linear binomials. Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic.

Learn how to factor quadratics that have the "perfect square" form and the "difference of squares" form. Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic.

Learn more ways to factor polynomials with degree higher than 2.

Practice proving polynomial identities, using all the factorization and expansion methods you know.

Prove more polynomial identities, this time including complex numbers!

Remember all these quadratic equations with "no real solution"? Well, it turns out those equations do have a solution, it's just a complex number! Solve a bunch of those here.

You may already have noticed that quadratic equations always have a solution when including complex number solutions. It turns out this is true for any polynomial equation, of any degree! Learn about this and more, right here.

Use all the knowledge you have about polynomials to find their zeros (which are the input values that make the polynomial equal to zero).

Learn how to use the zeros of polynomials to draw a pretty good sketch of their graphs.

Learn about the end behavior of polynomial functions. End behavior is the way the function behaves as the input values grow infinitely positive or infinitely negative.

Combine your knowledge about the zeros and the end behavior of a polynomial in order to sketch its graph.

You may already be familiar with types of symmetries of geometrical shapes. Learn how functions can be symmetrical too!

Learn how to determine the symmetry of a polynomial function.