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Polynomial Functions
A polynomial function of degree n is a function of
the form P(x) = a x n + a x n-1 + ...+ a x + a
n
n-1
1
where n is a nonnegative integer and an ≠ 0.
The numbers a0, a1,…, an are called the
coefficients of the polynomial.
The degree of a term is the exponent of the variable in
the term.
The degree of a polynomial is determined by the term
of highest degree.
A polynomial is written in standard form when the
terms are written in descending order of their
degree.
0
Classifying a polynomial by degree
Degree
Classification
Example
0
Constant
-3
1
Linear
8x
2
Quadratic
5x2 + x - 1
3
Cubic
-6x3 - 7
4
Quartic
x4 + x2 + 3x
5
Quintic
-x5 + x4 - 9
n
n-th degree
3x8
(8th degree)
Classifying a polynomial by number of
terms
# of terms
Classification
Example
1
Monomial
8x
2
Binomial
5x2 - 1
3
Trinomial
x4 + x2 + 3x
n
polynomial of 3x8 - x4 + x2 + 3x
n terms
(polynomial of 4 terms)
Ex 1: Write the polynomial in standard form, classify
it by its degree and number of terms.
a. -7x + 5x 3 - 6
5x 3 - 7x - 6
Cubic trinomial
b. x 2 - 4x + 3x 3 - 7x + 5x 3 - 6
c. 4x + 5 - 6x
8x + x -11x - 6
3
Cubic polynomial of
4 terms
-2x + 5
Linear binomial
d. 3x 2 + 4x - 8x + 2
2
3x - 4x + 2
2
Quadratic
trinomial
Ex 2: Write the polynomial in standard form, classify
it by its degree and number of terms.
a. x 2 -1- 3x 5 + 2x 2
b. -2x 3 - 7x 4 + x 3
-3x 5 + 3x 2 -1
Quintic Trinomial
-7x 4 - x 3
Quartic Binomial
x -2
3
c. 6x + x - 6x - 2
3
Cubic binomial
Suggested Assignment:
S 6-1 pg 309 – 310 #1-12, 25-30