Advanced Algebra
TASK - Classifying Polynomials
Name: ________________________________
Date: ___________________ Period: _______
A polynomial is a mathematical expression involving a sum of nonnegative integer powers in one or more
variables multiplied by coefficients. A polynomial in one variable with constant coefficients can be written
in a n x n  a n 1 x n 1  ...a 2 x 2  a1 x  a 0 form where an  0 , the exponents are all whole numbers, and the
coefficients are all real numbers.
1. What are whole numbers?
2. What are real numbers?
3. Decide whether each function below is a polynomial. If it is, write the function in standard form. If it is
not, explain why.
a. f ( x)  2 x 3  5x 2  4 x  8
b. f ( x)  2 x 2  x 1
c. f ( x)  5  x  7 x 3  x 2
d. f ( x) 
2 2
x  x 4  5  8x
3
e. f ( x)  2 x
g. f ( x) 
1
6
 2
2
x
3x
* A polynomial function in standard form is written in descending order of exponents from left to right.
* The degree is the highest exponent and will help us classify the polynomial.
* Coefficients are all real numbers. A leading coefficient is the number in front of the leading term when
in standard form.
* A constant term is a number without a variable.
Ex. f(x) = 2 + 3x
Ex. f(x) = 3x + x2 – 4 – 3x3
Standard Form:
Degree:
Leading Coefficient:
Constant:
Standard Form:
Degree:
Leading Coefficient:
Constant:
Classifying Polynomials by the number of terms:
1 Term:
2 Terms:
Monomial
Binomial
3 Terms:
4+ Terms:
Trinomial
Polynomial
Classifying Polynomials by the degree: The degree of the polynomial is the same as the term with the
highest degree.
Degree of 0:
Degree of 1:
Degree of 2:
Constant
Linear
Quadratic
Degree of 3:
Degree of 4:
Degree of 5:
Cubic
Quartic
Quintic
Polynomial
f ( x)  3 x  1
Number of Terms
Classification
Degree
Classification
f ( x)   x 5
f ( x)  8x 3  125
f ( x)  x 4  10 x 2  16
f ( x)  x 2  2 x  1
f ( x)  2
Practice:
State the degree and leading coefficient:
Degree:
LC:
Degree:
LC:
Degree:
LC:
Degree:
LC:
Degree:
LC:
Degree:
LC:
Write the function in standard form and identify the following:
Std Form:
LC:
Constant:
Degree:
# of Terms:
Classify by Degree:
Classify by Terms:
Std Form:
LC:
Constant:
Degree:
# of Terms:
Classify by Degree:
Classify by Terms:
Std Form:
LC:
Constant:
Degree:
# of Terms:
Classify by Degree:
Classify by Terms:
Std Form:
LC:
Constant:
Degree:
# of Terms:
Classify by Degree:
Classify by Terms:
Std Form:
LC:
Constant:
Degree:
# of Terms:
Classify by Degree:
Classify by Terms:
Std Form:
LC:
Constant:
Degree:
# of Terms:
Classify by Degree:
Classify by Terms: