3. Monomial: A number, a variable or the
product of a number and one or more
variables.
Polynomial: A monomial or a sum of monomials.
Binomial: A polynomial with exactly two
terms.
Trinomial: A polynomial with exactly three
terms.
Coefficient: A numerical factor in a term of
an algebraic expression.
4. Degree of a monomial: The sum of the
exponents of all of the variables in the
monomial.
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
decreasing order.
5. 1. A polynomial is a monomial or the sum of
monomials
2
4x 83 3
x 1425 2
xx
2 . Each monomial in a polynomial is a term
of the polynomial.
A. The number factor of a term is called the
coefficient.
B. The coefficient of the first term in a polynomial is the lead
coefficient.
3. A polynomial with two terms is called a
binomial.
4. A polynomial with three terms is called a
trinomial.
6. Write the polynomials in standard form.
745 24
xxx
4
4x 2
x x5 7
)7552(1 234
xxxx
4
x 3
2x 2
5x x5 7
Remember: The lead
coefficient should be
positive in standard
form.
To do this, multiply the
polynomial by –1
using the distributive
property
243
5572 xxxx
4
x 3
2x 2
5x x5 7
7. Write the polynomials in standard form and
identify the polynomial by degree and number
of terms.
23
237 xx
xx 231 2
8. 23
237 xx
3
3x 2
2x 7
7231 23
xx
723 23
xx
This is a trinomial. The trinomial’s degree is 3.
9. Add (x2 + x + 1) to (2x2 + 3x + 2)
You might decide to
add like terms as the
next slide demonstrates.
10. x2 + x + 1+ 2x2 + 3x + 2= 3x2+ 4x+3
Or you could add the
trinomials in a column
11. 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.
