The Basics of Polynomials
So far, you will have only dealt with equations that use variables without an exponent. From here on out, you will be dealing with much more complicated equations and pieces of equations. Because of this, you’ll need to learn the basics of working with and manipulating polynomials.
A polynomial is just some piece of an equation that uses variables, constants and basic mathematical operations like addition and multiplication. For example, x + 3 is a polynomial, and so is 7ab² + 4x³ – 3. That first polynomial x + 3 is pretty easy to understand and work with, and you have seen polynomials like this in the equations you have solved so far in Algebra 1. The second polynomial listed in our example, 7ab² + 4x³ – 3, is a bit more complicated.
To manage these complications, you have to learn how to do basic operations. First off, you’ll learn a little bit more about exponents and rules that you can use as shortcuts when dealing with them. Next, you’ll learn about like terms and addition and subtraction. This will teach you how to add and subtract polynomials from each other, much like you would just add or subtract two numbers. After addition and subtraction comes learning multiplication. You won’t be looking at division this early in your algebra career since there are other topics you have to learn first because of something special that happens with the division of polynomials.
After learning about the multiplication of polynomials, you’ll learn some basics of how to deal with square roots and other radicals with regular numbers and variables. Afterwards, you’ll learn to apply this knowledge to polynomials. Once you’re at this point, you’ll have a much greater understanding of how to deal with equations, and a lot of the anxiety and fear that Algebra 1 students typically get will be gone.
Learning how to deal with polynomials is super important because everything left in Algebra 1 depends on them. If you don’t pick up these basics now, then you’re going to be completely lost as you go on through the rest of Algebra 1 and into other math classes. Learn the basics now and you will save yourself a lot of time, trouble, effort and headache in the future.
The Rules of Exponents – There are some special rules and patterns that come into play when handling exponents.
Like Terms – Another look at like terms in the context of polynomial operations.
Addition and Subtraction of Polynomials – The process of simplifying polynomials starts with addition and subtraction.
Multiplication of Polynomials – Multiplying polynomials is slightly more complicated than multiplying numbers.
Radical Simplification and Operations – Dealing with terms that include the radical sign (square root sign) isn’t as hard as it looks.