2. 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.
3. 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.
4. What is the degree of the monomial?
2
4
5 b
x
The degree of a monomial is the sum of the
exponents of the variables in the monomial.
The exponents of each variable are 4 and 2. 4+2 = 6.
The degree of the monomial is 6.
The monomial can be referred to as a sixth
degree monomial.
5. A polynomial is a monomial or the sum of
monomials
2
4x 8
3 3
x 14
2
5 2
x
x
Each monomial in a polynomial is a term of the
polynomial.
The number factor of a term is called the
coefficient.
The coefficient of the first term in a polynomial is
the lead coefficient.
A polynomial with two terms is called a binomial.
6. 1
4
x
8
3 3
x
14
2
5 2
x
x
The degree of a polynomial in one variable is the
largest exponent of that variable.
2 A constant has no variable. It is a 0 degree polynomial.
This is a 1st
degree polynomial. 1st
degree polynomials are
linear.
This is a 2nd
degree polynomial. 2nd
degree
polynomials are quadratic.
This is a 3rd
degree polynomial. 3rd
degree polynomials
are cubic.
7. Classify the polynomials by degree and number of terms.
Polynomial
a.
b.
c.
d.
5
4
2
x
x
x
2
3
1
4 2
3
x
x
Degree
Classify by
degree
Classify by
number of
terms
Zero Constant Monomial
First Linear Binomial
Second Quadratic Binomial
Third Cubic Trinomial
8. To rewrite a polynomial in standard form,
rearrange the terms of the polynomial starting with
the largest degree term and ending with the lowest
degree term.
The leading coefficient, the coefficient of the first
term in a polynomial written in standard form,
should be positive.
9. 7
4
5 2
4
x
x
x
x
5
4
4x 2
x
7
Write the polynomials in standard form.
2
4
3
5
5
7
2 x
x
x
x
3
2x
4
x
7
x
5
2
5x
)
7
5
5
2
(
1 2
3
4
x
x
x
x
3
2x
4
x 7
x
5
2
5x
Remember: The lead
coefficient should be
positive in standard
form.
To do this, multiply the
polynomial by –1 using
the distributive
property.
10. Write the polynomials in standard form and identify
the polynomial by degree and number of terms.
2
3
2
3
7 x
x
1.
2. x
x 2
3
1 2
11. 2
3
2
3
7 x
x
2
3
2
3
7 x
x
3
3x
2
2x
7
7
2
3
1 2
3
x
x
7
2
3 2
3
x
x
This is a 3rd
degree, or cubic,
trinomial.
12. x
x 2
3
1 2
x
x 2
3
1 2
2
3x x
2
1
This is a 2nd
degree, or quadratic, trinomial.
