# Examples of Monomials and Polynomials

Updated May 11, 2021
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chart showing monomial, binomial and trinomial terms
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Created by Beth Wiggins, Owned by YourDictionary, Copyright YourDictionary

A monomial is an expression in algebra that contains one term, like 3xy. Monomials include numbers, whole numbers and variables that are multiplied together, and variables that are multiplied together. A polynomial is a sum of monomials where each monomial is called a term. Read more about the difference between monomials and polynomials, the rules for each term and several helpful examples.

## Identifying a Monomial

Finding a monomial is easier than it seems. "Mono" means one, meaning that "monomial" includes only one term. It is a piece of a polynomial. Monomials can include these characteristics:

• any number by itself (such as 5, 2700 or 83)
• a variable (such as "b" or "x")
• a coefficient that multiplies the variable (such as the 4 in "4x")
• positive exponents (such as the 2 in 7x2)
• a combination of these (such as 98b or 78xyz)

Monomials cannot have a fractional or negative exponent. Monomial examples include:

• 6xy3
• 948
• 2y3z2
• a2
• -7b
• y
• 36
• -12x
• a8b4c2
• 72a

A monomial multiplied by a monomial is also a monomial. A monomial multiplied by a constant (not variable) is also a monomial. When looking at examples of monomials, you need to understand different types of polynomials, which have more than one term (since "poly" means "many.") Following is an explanation of polynomials, binomials, trinomials, and degrees of a polynomial.

## Identifying a Polynomial

A polynomial shows the sum of monomials. It is an algebraic expression with a finite number of terms. Because a polynomial is made of monomials, it also cannot have negative exponents.

Polynomial examples include:

• 7a2 + 18a - 2
• -2x5 + 17x3 - 9x
• 5a - 12
• 6m4 - 3n
• 11x2 + 3b − 4b3 + 10
• x - y
• 8a5 - 7a
• -2x9 + x3 + x2
• 12a + 14b
• 9 + 9a2

### Types of Polynomials

If you notice that these polynomials have different terms, that's because they're different types of polynomials.

• binomials - a polynomial with two terms (such as in 3x + 1 and 2 - 5x)
• trinomials - a polynomial with three terms (such as 2x2 + 4x - 11 and 4x3 - 13x + 9)

When a polynomial has four terms (such as 5x6 - 17x2 + 97 + 24x), it's sometimes called a quadrinomial. However, larger polynomials are usually known as four-term polynomials, five-term polynomials, and so on.

## Degrees of Monomials and Polynomials

The degree of a monomial or polynomial is the highest power of the variable in that polynomial, as long as there is only one variable. If there is more than one variable, you add up the exponents for all the variables to find the degree.

If a polynomial has more than one variable, then you can find the degree of by looking at each monomial. For example: 14x4 + 27x2y - y has the degree of 4. Looking at each individual term, you find that the exponents are 4, 3 (2+implicit 1), and 1). 4 is the highest, so the degree is 4.

For example:

• The degree of the monomial 8xy2 is 3, because x has an implicit exponent of 1 and y has an exponent of 2 (1+2 = 3).
• The degree of the polynomial 7x3 - 4x2 + 2x + 9 is 3, because the highest power of the only variable x is 3.
• The degree of the polynomial 18s12 - 41s5 + 27 is 12. There is one variable (s) and the highest power of s here is 12.
• The degree of the polynomial 8z + 2008 is 1, because z is the only variable and is in the first power.