Monomial Definition: (the prefix โmonoโ 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:
2๐ฅ โ3๐ฅ๐ฆ 1
2๐ฅ2 โ5 7๐ฅ4
Polynomial Definition: (the prefix โpolyโ means many)
A sum or difference of monomials. The exponent of each variable must be a non-negative
integer.
Examples of Polynomials:
2๐ฅ โ 4 6๐ฅ2โ 7๐ฅ + 2 ๐ฅ3โ 2๐ฅ 2+11๐ฅ โ 1
Examples of NON-Polynomials:
log(๐ฅ + 5) 2๐ฅ+ 5 ๐ฅ2+1
๐ฅ โ๐ฅ + 5๐ฅ โ 3 6๐ฅ3+๐ฅ1
2+ 5 |๐ฅ + 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 โ ๐ฅ0= 7 โ 1= 7)
2๐ฅ โ 4 has a degree of 1
6๐ฅ2โ 7๐ฅ + 2 has a degree of 2
๐ฅ3โ 2๐ฅ2 has a degree of 3
๐ฅ + 5๐ฅ3โ 2๐ฅ 4โ10๐ฅ2 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, 3๐ฅ โ 7๐ฅ3+ 9 โ 2๐ฅ4โ ๐ฅ2 is NOT in standard form.
It should be written as: โ2๐ฅ4โ 7๐ฅ3โ ๐ฅ 2+ 3๐ฅ + 9
