2. Definitions
A monomial is a real number, a
variable, or a product of a real number
and one or more variables with whole
number exponents.
2 3
◦ Examples: 5, x, 3wy , 4 x
The degree of a monomial in one
variable is the exponent of the variable.
3. Definitions
A polynomial is a monomial or a sum of
monomials.
◦ Example: 3 xy + 2 x − 5
2
The degree of a polynomial in one
variable is the greatest degree among its
monomial terms.
◦ Example: −4 x − x + 7
2
4. Definitions
A polynomial function is a polynomial
of the variable x.
◦ A polynomial function has distinguishing
“behaviors”
The algebraic form tells us about the graph
The graph tells us about the algebraic form
5. Definitions
The standard form of a polynomial
function arranges the terms by degree in
descending order
◦ Example: P( x) = 4 x + 3x + 5 x − 2
3 2
6. Definitions
Polynomials are classified by degree and
number of terms.
◦ Polynomials of degrees zero through five have
specific names and polynomials with one
through three terms also have specific names.
Degree Name Number of Name
0 Constant Terms
1 Linear 1 Monomial
2 Quadratic 2 Binomial
3 Cubic 3 Trinomial
4 Quartic 4+ Polynomial with ___ terms
5 Quintic
8. Example
Write each polynomial in standard form.
Then classify it by degree and by number
of terms.
3 − 4 x + 2 x +10
5 2
9. Polynomial Behavior
The degree of a polynomial function
◦ Affects the shape of its graph
◦ Determines the number of turning points
(places where the graph changes direction)
◦ Affects the end behavior (the directions of
the graph to the far left and to the far right)
10. Polynomial Behavior
The graph of a polynomial function of
degree n has at most n – 1 turning points.
◦ Odd Degree = even number of turning points
◦ Even Degree = odd number of turning points
Think about this:
◦ If a polynomial has degree 2, how many
turning points can it have?
◦ If a polynomial has degree 3, how many
turning points can it have?
14. Example
Determine the end behavior of the graph
of each polynomial function.
y = −2 x + 8 x − 8 x + 2
4 3 2
15. Increasing and Decreasing
Remember: We read from left to right!
A function is increasing when the y-
values increase as the x-values increase
A function is decreasing when the y-
values decrease as the x-values increase
