Math 154
Elementary Algebra
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Polynomials—6.3
Definitions
A term is a constant or a product of a constant and a variable or a product of variables that are raised to powers.
Terms are separated by addition.
A monomial is a single term that only has whole number powers.
The degree of a monomial is the sum of the exponents of the variables.
The coefficient of a term is the constant part of a term.
A polynomial is a monomial or a sum of monomials.
The leading term of a polynomial is the term of the highest degree.
The leading term¶VFRHIILFLHQWLVWKHleading coefficient of the polynomial.
7KHOHDGLQJWHUP¶VGHJUHHLVWKHdegree of the polynomial.
A polynomial of degree 0 or 1 is called linear.
A polynomial of degree 2 is called quadratic.
A polynomial of degree 3 is called cubic.
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a trinomial.
Polynomials are usually arranged in descending order, so that the exponents of a certain variable decrease from left
to right.
1.
For each polynomial given, find the degree of each term, the degree of the polynomial, the leading term, and the leading
coefficient. If the polynomial has a specific name²monomial, binomial, or trinomial²give that name.
a)
Individual
Terms
The Degree of Each
Individual Term
The Coefficient of Each
Individual Term
The Leading Coefficient
of the Polynomial
The Degree of
the Polynomial
Specific Name of
the Polynomial
The Degree of Each
Individual Term
The Coefficient of Each
Individual Term
The Leading Coefficient
of the Polynomial
The Degree of
the Polynomial
Specific Name of
the Polynomial
b)
Individual
Terms
2.
Arrange each polynomial in descending order. Give the degree of each polynomial.
a)
b)