# Polynomial expressions, equations, & functions

This topic covers: - Adding, subtracting, and multiplying polynomial expressions - Factoring polynomial expressions as the product of linear factors - Dividing polynomial expressions - Proving polynomials identities - Solving polynomial equations & finding the zeros of polynomial functions - Graphing polynomial functions - Symmetry of functions

This course contains 37 segments:

**Intro to polynomials**

Learn about polynomial expressions: What are they? How are they constructed? What can we do with them?

**Adding & subtracting polynomials**

Learn how to add and subtract polynomial expressions with one variable.

**Adding & subtracting polynomials: two variables**

Learn how to add and subtract polynomial that involve two variables. For example, x^3 + xy + 3y - (x^3 + 6xy + 2y^2).

**Multiplying monomials**

As an intro to more elaborate polynomial multiplication, learn how to multiply monomials (which are polynomials with a single term). For example, multiply 2x³ and 5x⁷.

**Multiplying monomials by polynomials**

Learn how to multiply a polynomial expression by a monomial expression. Monomials are just polynomials with a single term!

**Multiplying binomials**

Learn how to multiply two binomials together. For example, (3x - 7) * (10x + 2).

**Special products of binomials**

Learn about the special types of products of binomials: perfect squares and the difference of two squares. These will be very helpful once you tackle more advanced expressions in Algebra.

**Multiplying binomials by polynomials**

Learn how to multiply a polynomial expression by a binomial expression.

**Polynomials word problems**

See a few examples of how we can represent real-world situations with polynomials.

**Introduction to factorization**

Learn what factorization is all about, and warm-up by factoring some monomials.

**Factoring monomials**

Learn how to write a monomial as a factor of two other monomials. For example, write 12x^3 as (4x)(3x^2).

**Factoring polynomials by taking common factors**

Learn how to take a common monomial factor out of a polynomial expression. For example, write 2x^3+6x^2+8x as (2x)(x^2+3x+4).

**Evaluating expressions with unknown variables**

Learn how to evaluate expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=3, evaluate 4a+4b.

**Factoring quadratics intro**

Learn how to factor quadratic expressions with a leading coefficient of 1. For example, factor x²+3x+2 as (x+1)(x+2).

**Factoring quadratics by grouping**

Learn how to factor quadratic expressions with a leading coefficient other than 1. For example, factor 2x²+7x+3 as (2x+1)(x+3).

**Factoring polynomials with quadratic forms**

Learn how to factor quadratic polynomials of the form ax^2+bx+c as the product of two linear binomials. For example, write x^2+3x-10 as (x+5)(x-2). Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic. For example, write x^4-4x^2-12 as (x^2+2)(x^2-6).

**Factoring quadratics: Difference of squares**

Learn how to factor quadratics that have the "difference of squares" form. For example, write x²-16 as (x+4)(x-4). Learn how to identify this form in more elaborate expressions. For example, write 4x²-49 as (2x+7)(2x-7).

**Factoring quadratics: Perfect squares**

Learn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)². Learn how to identify these forms in more elaborate expressions. For example, write 4x²+28x+49 as (2x+7)².

**Strategy in factoring quadratics**

There are a lot of methods to factor quadratics, which apply on different occasions and conditions. Now that we know all of them, let's think strategically about which of them is useful for a given quadratic expression we want to factor.

**Factoring polynomials with special product forms**

Factor polynomials of various degrees using factorization methods that are based on the special product forms "difference of squares" and "perfect squares." For example, factor 25x⁴-30x²+9 as (5x²-3)².

**Long division of polynomials**

Learn how to divide two polynomials using long division.

**Synthetic division of polynomials**

Learn how to divide polynomials using long division.

**Practice dividing polynomials with remainders**

After learning about the different methods in which we can find the quotient and the remainder of two polynomials, gain some practice with actually performing polynomial division yourself.

**Polynomial Remainder Theorem**

The polynomial remainder theorem allows us to easily determine whether a linear expression is a factor of a given polynomial. Learn exactly what the theorem means, practice using it, and learn about its proof.

**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!

**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.

**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.

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Length | 37 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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Rating | Not enough ratings |
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Length | 37 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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