Algebra
Polynomial basics
"Polynomials" sound like a fancy word, but you just have to break down the root words. "Poly" means "many". So we're just talking about "many nomials" and everyone knows what a "nomial" is. Okay, most of us don't. Well, a polynomials has "many" terms.
From understanding what a "term" is to basic simplification, addition and subtraction of polynomials, this tutorial will get you very familiar with the world of many "nomials." :)
- Terms coefficients and exponents in a polynomial
- Interesting Polynomial Coefficient Problem
- Polynomials1
- Polynomials 2
- Evaluating a polynomial at a given value
- Simplify a polynomial
- Adding Polynomials
- Example: Adding polynomials with multiple variables
- Addition and Subtraction of Polynomials
- Adding and Subtracting Polynomials 1
- Adding and Subtracting Polynomials 2
- Adding and Subtracting Polynomials 3
- Subtracting Polynomials
- Subtracting polynomials with multiple variables
- Adding and subtracting polynomials
Multiplying monomials, binomials and polynomials in general
No algebraic arsenal is complete without the ability to multiply expressions. In this tutorial, we'll review some basic exponent properties and the distributive property when multiplying single terms. We'll then see that multiplying anything fancier (binomials, polynomials, etc.) is just an extension of the distributive property that you first learned in elementary school. We do cover the FOIL method as well because some schools teach this, but we think it is lame and not real learning. The distributive property is FAR more powerful and general.
- Multiplying Monomials
- Dividing Monomials
- Multiplying and Dividing Monomials 1
- Multiplying and Dividing Monomials 2
- Multiplying and Dividing Monomials 3
- Monomial Greatest Common Factor
- Factoring and the Distributive Property
- Factoring and the Distributive Property 2
- Factoring and the Distributive Property 3
- Multiplying Binomials with Radicals
- Multiplication of Polynomials
- Multiplying Binomials
- Multiplying Polynomials1
- Multiplying Polynomials 2
- Square a Binomial
- Special Products of Binomials
- Special Polynomials Products 1
- Factor polynomials using the GCF
- Special Products of Polynomials 1
- Special Products of Polynomials 2
- Multiplying expressions 0.5
- Factoring linear binomials
- Multiplying expressions 1
- Multiplying Monomials by Polynomials
- Multiplying Polynomials
- Multiplying Polynomials 3
- More multiplying polynomials
- Multiplying polynomials
- Level 1 multiplying expressions
Dividing polynomials
You know what polynomials are. You know how to add, subtract, and multiply them. Unless you are completely incurious, you must be wondering how to divide them!
In this tutorial we'll explore how we divide polynomials--both through algebraic long division and synthetic division. (We like classic algebraic long division more since you can actually understand what you're doing.)
- Polynomial Division
- Polynomial divided by monomial
- Dividing multivariable polynomial with monomial
- Dividing polynomials 1
- Dividing polynomials with remainders
- Synthetic Division
- Synthetic Division Example 2
- Why Synthetic Division Works
- Factoring Sum of Cubes
- Difference of Cubes Factoring
- Algebraic Long Division
- Algebra II: Simplifying Polynomials