Polynomials -Understand The Little Things Before Mastering The Big Stuff

One of the biggest topics we study in algebra is polynomials.  Almost half of what your homeschooler will learn in algebra is focused on polynomials so it’s a good idea for us to really understand what one is.
I’m sure most of you out there have seen the word “polynomial” but do you know what one is? Take a second and see if you can define a polynomial (this would be a good pop quiz for your child) by writing examples.  Let’s jump into the definition of a polynomial.

First the technical definition:

(remember- Real Numbers are all the numbers on the number line to include integers, fractions, decimals, square roots, etc. )

A polynomial in the variable x is defined below where “a” is any Real Number and “k” is a positive integer









Easy to understand examples of what is and is not a polynomial- focus on the power:



** the reason the examples in the right side column fail is because the exponents are not positive integers ** 

Polynomials are the basic building blocks of algebra.  The most basic polynomials have 1 term- like these examples.  However we can combine “basic polynomial terms” into larger more complex polynomials so the fun is endless when it comes to polynomials.