Polynomials

Heads up! This course may be archived and/or unavailable.

This course is a part of Algebra II, a 23-course Topic series from Khan Academy.

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.

This course contains 15 segments:

The binomial theorem

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

Understanding 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!

Factoring polynomials - Quadratic forms

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.

Factoring polynomials - Special product forms

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.

Advanced polynomial factorization methods

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

Proving polynomial identities

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

Polynomial identities with complex numbers

Prove more polynomial identities, this time including complex numbers!

Quadratic equations with 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.

The Fundamental Theorem of Algebra

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.

Finding zeros of polynomials

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

Zeros of polynomials and their graphs

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

End behavior of polynomial functions

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.

Graphs of polynomials

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

Introduction to symmetry of functions

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

Symmetry of polynomial functions

Learn how to determine the symmetry of a polynomial function.