Vocabulary A monomial is a number a variable
Vocabulary • A monomial is a number, a variable, or a product of numbers and variables with whole number exponents. • If the monomial includes variables, the number part is called the coefficient of the term and is written first. • A number by itself is called a constant. • The degree of the monomial is the sum of the exponents in the monomial. FHS Polynomials 1
Examples • Find the coefficient and the degree of each of the following: coefficient: 8 degree: 5 coefficient: - 4 degree: 7 coefficient: 1 degree: 3 coefficient: constant degree: 0 FHS Polynomials 2
Vocabulary • A polynomial is a monomial or a sum or difference of monomials and constants. • Each of the monomials or constants is called a term. The degree of a polynomial is the degree of the term with the greatest degree. • The standard form of a polynomial is written with the terms in order from the greatest degree to the least degree. The coefficient of the first term is called the leading coefficient. FHS Polynomials 3
Example • Write { { { each { Find the degree of term. in standard form. 1 3 0 4 Write the terms in order of degree. The leading coefficient is 2. FHS Polynomials 4
Vocabulary • Polynomials have special names based on their degree. Degree Name FHS 0 1 2 3 constant linear quadratic cubic 4 5 6 or more quartic quintic 6 th degree, 7 th. . . Polynomials 5
Vocabulary • Polynomials also have special names based on the number of terms they have. Terms Name 1 2 3 4 or more monomial binomial trinomial polynomial • What is the name of the following polynomial based on the degree and the number of terms? a quartic trinomial FHS Polynomials 6
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