This document discusses polynomials and how to identify and analyze them. It defines a polynomial as a monomial or a sum of monomials, and specifies that an expression is not a polynomial if it has a variable in the denominator. It provides rules for determining the degree of a term, monomial, and polynomial. Specifically, it states that the degree of a polynomial is the greatest degree of any term. Examples are given to demonstrate how to identify if an expression is a polynomial and determine its degree.

2. Objectives
We must be able to :
 Analyze the given term whether its
POLYNOMIAL or NOT POLYNOMIAL.
 Identifying the degree of a polynomial.

3. What does each
prefix mean?
mono
one
bi
two
tri
three

4. What about poly?
one or more
A polynomial is a monomial or a
sum/difference of monomials.
An expression is not a polynomial if
there is a variable in the denominator.

5. POLYNOMIAL OR NOT
POLYNOMIAL
1) 7y - 3x + 4
trinomial
2) 10x3yz2
monomial
3) 3X-X⅞
not a polynomial

7. RULES
 If a term in a polynomial has one variable
as a factor, then the degrees of that term
is the power of the variable.
 If two or more variables are present in
term as a factor, the degree of the term is
the sum of the power of the variables.
 The degree of a polynomial is the greatest
degree of any term in a polynomial.
 Any non-zero constant is defined to be a
polynomial of degree zero.

8. The degree of a monomial is the sum of
the exponents of the variables.
1) 5x2
2
2) 4a4b3c
8
3) -3
0

9. To find the degree of a polynomial,
find the largest degree of the
terms.
1) 8x2 - 2x + 7
Degrees: 2 1 0
Which is biggest? 2 is the degree!
2) y7 + 6y4 + 3x4m4
Degrees: 7 4 8
8 is the degree!

10. Determine which of the following are
polynomial functions. If the function is a
polynomial, state its degree.
f ( x) = 2x − x
4
A polynomial of degree 4.
We can write in an x0 since this = 1.
g ( x) = 2 x 0 A polynomial of degree 0.
Not a polynomial because of the square root
h( x ) = 2 x + 1
since the power is NOT an integer
1
x=x 2
3
F ( x) = + x
Not a polynomial because of the x in the
2 denominator since the power is negative
1
x =x −1
x

11. PREPARED BY :
Alay,Helen Grace A.

12. 09302012