Definition of a polynomial
Before giving you the definition of a polynomial, it is important to provide the definition of a monomial
Definition of a monomial:
A monomial is a variable, a real number, or a multiplication of one or more variables and a real number with wholenumber exponents
Examples of monomials and nonmonomials
Monomials

9

x

9x

6xy

0.60x^{4}y

Not monomials

y  6

x^{1} or 1/x

√(x) or x^{1/2}

6 + x

a/x

Polynomial definition:
A polynomial is a monomial or the sum or difference of monomials. Each monomial is called a term of the poynomial
Important!:Terms are seperated by addition signs and subtraction signs, but never by multiplication signs
A polynomial with one term is called a monomial
A polynomial with two terms is called a binomial
A polynomial with three terms is called a trinomial
Examples of polynomials:
Polynomial

Number of terms

Some examples

Monomial

1

2, x, 5x^{3}

Binomial

2

2x + 5, x^{2}  x, x  5

Trinomial

3

x^{2} + 5x + 6, x^{5}  3x + 8

Difference between a monomial and a polynomial:
A polynomial may have more than one variable.
For example, x + y and x
^{2} + 5y + 6 are still polynomials although they have two different variables x and y
By the same token, a monomial can have more than one variable. For example, 2 × x × y × z is a monomial
Exercices
For all expressions below, look for all expressions that are polynomials.
For those that are polynomials, state whether the polynomial is a monomial, a binomial, or a trinomial
1) 3.4 + 3.4x
2) z
^{2} + 5z
^{1} + 6
3) 8
4) 2c
^{2} + 5b + 6
5) 14 + x
6) 5x  2
^{1}
7) 4 b
^{2}  2 b
^{2}
8) f
^{2} + 5f + 6
Answer: 1), 3), 4), 5), 6), and 8) are polynomials.
1), 5), and 6) are binomials. 3) is a monomial. 4) and 8) are trinomials
2) and 7) are not because they have negative exponents
Notice that 6) is still a polynomial although it has a negative exponent. It is because it is the exponent of a real number, not a variable
In fact, 5x  2
^{1} = 5x + 1/2 = 5x + 0.5
It is subtle, but if you have any questions about the definition of a polynomial, feel free to contact me.
Definition of a polynomial quiz

Apr 03, 17 09:12 AM
Learn to divide using partial quotients. Understand the concept fast!
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.