As you have already noticed, algebraic expressions may contain one or more terms.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Remember, addition and subtraction are what separates terms, and help us in discovering the size of a polynomial.
What is a polynomial?
Simply put, a polynomial means “many terms,” and all polynomials are classified by their size:
- Monomial = one term
- Binomial = two terms (two monomials added together)
- Trinomial = three terms (three monomials added together)
- Polynomial = four or more terms
It is important to note that a monomial is an algebraic expression that is a numeral (constant), a variable, or a product of a numeral and one or more variables.
Polynomial Function Formula
Additionally, all variables in a polynomial must always have non-negative, integer exponents.
What does that mean?
The exponents on any variable must be positive integers, and variables can never be in the denominator.
This lesson goes into great detail on how to classify polynomials by their size (number of terms) and degree.
We will learn:
- How to find the degree of a monomial (one term).
- How to find the degree of a Polynomial.
Is there a difference?
Yes!
The degree of a monomial is the sum of all the variable exponents in the monomial.
The degree of a polynomial is the greatest of the degrees of its terms after it has been simplified.
How do we simplify a polynomial?
Well, a polynomial is in simplest form when no two of its terms are similar. Consequently, we will learn how to add and subtract Polynomials.
Don’t worry; you already know how to do this!
To add or subtract polynomials all we have to do is add or subtract the coefficients of any like terms, as Math is Fun accurately states.
We will also learn how to write a polynomial in Standard Form.
Meaning we will place the terms of the polynomial in descending order of degree from left to right, for the variable that comes first alphabetically.
Lastly, we will wrap things up with a review of how to solve equations, but this time we will spend more time on adding and subtracting polynomial expressions before solving for the unknown variable.
Adding and Subtracting Polynomials – Video
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