Monomial: A number, a variable or the
product of a number and one or more
Polynomial: A monomial or a sum of monomials.
Binomial: A polynomial with exactly two
Trinomial: A polynomial with exactly three
Coefficient: A numerical factor in a term of
an algebraic expression.
Degree of a monomial: The sum of the
exponents of all of the variables in the
Degree of a polynomial in one variable:
The largest exponent of that variable.
Standard form: When the terms of a
polynomial are arranged from the largest
exponent to the smallest exponent in
1. A polynomial is a monomial or the sum of
4x 83 3
x 1425 2
2 . Each monomial in a polynomial is a term
of the polynomial.
A. The number factor of a term is called the
B. The coefficient of the first term in a polynomial is the lead
3. A polynomial with two terms is called a
4. A polynomial with three terms is called a
Write the polynomials in standard form.
x x5 7
5x x5 7
Remember: The lead
coefficient should be
positive in standard
To do this, multiply the
polynomial by –1
using the distributive
5x x5 7
Write the polynomials in standard form and
identify the polynomial by degree and number
xx 231 2
This is a trinomial. The trinomial’s degree is 3.
Add (x2 + x + 1) to (2x2 + 3x + 2)
You might decide to
add like terms as the
next slide demonstrates.
x2 + x + 1+ 2x2 + 3x + 2= 3x2+ 4x+3
Or you could add the
trinomials in a column
Dividing a polynomial by a
polynomial other than a
monomial uses a “long
division” technique that is
similar to the process known as
long division in dividing two
numbers, which is reviewed on
the next slide.