When it comes to writing polynomials, it can be challenging to know in which order to write all of the terms. Today, we will be discussing, explaining, and sharing examples on how to properly write a polynomial in standard form. But first things first, what is standard form?
In order to write a polynomial in standard form, you must write the terms from the largest degree to the smallest degree. Let's take a look at an example.
In this example, we see a polynomial expression written in standard form as well as a table to help us understand why. The first step is determining the degree of each term. The first term, 5x^3 has x raised to the 3rd power so it is degree 3. The second term 2x has x raised to the 1st power so it is degree 1 (NOTE: when x is raised to the 1st power, we do not write the 1). And finally, the last term, 4, has x raised to the 0 power so it is degree 0 (NOTE: when x is raised to the 0 power, it is always equal to 1 so you will not see a variable in the term). After determining the degree of each term, the final step is writing the polynomial in order from the greatest power to the smallest power. So in this case, it would be 5x^3 + 2x + 4. And there you have it: a polynomial in standard form!
Why Use Standard Form?
Standard form is a helpful way to write polynomials because it creates a level of consistency and predictability in algebra. For example, if you and your friend were to solve an equation resulting in a polynomial expression and wanted to compare, it would be much easier to tell if you got the same result if you both wrote your expression in standard form. Otherwise, you would have to go term by term and that just takes more time!
Q: Are these polynomial expressions the same? It would be much easier to tell if they were both written in standard form!