Polynomial

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 whole-number exponents

Examples of monomials and non-monomials

Monomials	9	x	9x	6xy	0.60x4y
Not monomials	y - 6	x-1 or 1/x	√(x) or x1/2	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, 5x3
Binomial	2	2x + 5, x2 - x, x - 5
Trinomial	3	x2 + 5x + 6, x5 - 3x + 8

Difference between a monomial and a polynomial:

A polynomial may have more than one variable.

For example, x + y and x² + 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) z² + 5z^-1 + 6

3) -8

4) 2c² + 5b + 6

5) 14 + x

6) 5x - 2^-1

7) 4 b² - 2 b^-2

8) f² + 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