Monomial Definition: (the prefix “mono” means one) a monomial is a constant or variable or a
multiple of such (i.e., just one term) Variables can only have exponents that are non-negative
integers.
Examples of monomials:
2𝑥 −3𝑥𝑦 1
2𝑥2 −5 7𝑥4
Polynomial Definition: (the prefix “poly” means many)
A sum or difference of monomials. The exponent of each variable must be a non-negative
integer.
Examples of Polynomials:
2𝑥 − 4 6𝑥2− 7𝑥 + 2 𝑥3− 2𝑥 2+11𝑥 − 1
Examples of NON-Polynomials:
log(𝑥 + 5) 2𝑥+ 5 𝑥2+1
𝑥 √𝑥 + 5𝑥 − 3 6𝑥3+𝑥1
2+ 5 |𝑥 + 5|
The DEGREE of a polynomial is the highest exponent.
For example, the following polynomials have the following DEGREES:
7 has a degree of 0 (because 7 ∙ 𝑥0= 7 ∙ 1= 7)
2𝑥 − 4 has a degree of 1
6𝑥2− 7𝑥 + 2 has a degree of 2
𝑥3− 2𝑥2 has a degree of 3
𝑥 + 5𝑥3− 2𝑥 4−10𝑥2 has a degree of 4
Standard Form of a Polynomial:
Polynomials should always be written in standard form. Standard form is when each term is written in
descending order of its exponent.
For example, 3𝑥 − 7𝑥3+ 9 − 2𝑥4− 𝑥2 is NOT in standard form.
It should be written as: −2𝑥4− 7𝑥3− 𝑥 2+ 3𝑥 + 9
