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Some expressions that are polynomials are
.
A fraction occurs, but no variable appears in the denominator.
Some expressions that are not polynomials are
.
A variable appears in the denominator.
.
A negative exponent appears on a variable.
Polynomials can be classified using two criteria: the number of terms and degree of the polynomial.
Number of Terms | Name | Example | Comment |
One | Monomial | mono means “one” in Greek. | |
Two | Binomial | bi means “two” in Latin. | |
Three | Trinomial | tri means “three” in Greek. | |
Four or more | Polynomial | poly means “many” in Greek. |
is a monomial of degree 3.
is a monomial of degree 5.
is a monomial of degree 2.
8 is a monomial of degree 0. We say that a nonzero number is a term of 0 degree since it could be written as . Since , . The exponent on the variable is 0 so it must be of degree 0. (By convention, the number 0 has no degree.)
is a monomial of the first degree. could be written as . The exponent on the variable is 1 so it must be of the first degree.
is a monomial of degree . This is a 7th degree monomial.
is a monomial of degree . This is a 12th degree monomial.
is a monomial of degree . This is a 2nd degree monomial.
is a trinomial of degree 3. The first term, , is the term of the highest degree. Therefore, its degree is the degree of the polynomial.
is a binomial of degree 4.
is a trinomial of degree 2.
is a polynomial of degree 7.
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