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.