Polynomial Notes
•
COEFFICIENT is the __________________________________________ of the variable.
•
DEGREE ---is the ________________________________________________ of the variables.
ADD THE TOTAL EXPONENTS _______________________________________
•
TERM --is an expression that is ______________________________________________________
•
CONSTANT --is the ____________________________________________ of the equation that
_________________________ have the variable.
•
STANDARD FORM ---is __________________________________ form in equation. __________________________
Identify the degree of each monomial
A. z 6
D. a 2bc 3
C. 8xy3
B. 5.6
A ____________________ __________ is given by the term with the greatest degree. A polynomial with one
variable is in standard form when its terms are written in ____________________________________________.
So, in standard form, the degree of the _______________________ indicates the degree of the polynomial,
and the _______________________ ______ is the coefficient of the first term.
3
2
Standard Form: 5 x  8 x  3x  17
Degree of polynomial: ___________
Leading Coefficient: ___________
A polynomial can be classified by
A polynomial can be classified by
____________________________________________
______________________________________________
Number
of
Terms
Degree
Name
Name
1st
1
2nd
2
3rd
3
4th
4 or more
5th and
beyond
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of
terms. Name the polynomial.
A.
3  5x2  4x
____________________________
B.
3x2  4  8x4 ______________________________
Leading coefficient: ____________
Leading coefficient:_____________
Degree: ___________
Degree: ____________
Terms: ___________
Terms: ____________
Name: ________________________________
Name: ___________________________________
End Behavior of a graph describes the _______________________________________________________________________
To describe a graph without plugging into the calculator,

we need to look at the polynomial’s ______________________________________________________
If the leading coefficient is:

Positive---the right side of the graph will ____________________

Negative---the right side of the graph will ____________________
If the Highest Degree is:

Even----then the LEFT side and the RIGHT side are ________________________________

Odd----then the LEFT side and the RIGHT side are ________________________________
f (x)  4x3  3x
Determine the End Behavior of
the following.
Example 1
f ( x)  4x 4  2x3  6x  3
Leading Coefficient ___________________
Degree ________________________________
Right side ______________________________
Left side ______________________________
As x  , then P  x   _______
As x  , then P  x   _______
Example 2 f ( x)  3x7  8x 2  4x  13
Leading Coefficient ___________________
Degree ________________________________
Right side ______________________________
Left side ______________________________
As x  , then P  x   _______
As x  , then P  x   _______
Example 3 f ( x)  2x5  x4  6x2  8x
Example 4 f ( x)  2x 2  6x  6
Leading Coefficient ___________________
Leading Coefficient ___________________
Degree ________________________________
Degree ________________________________
Right side ______________________________
Right side ______________________________
Left side ______________________________
Left side ______________________________
As x  , then P  x   _______
As x  , then P  x   _______
As x  , then P  x   _______
As x  , then P  x   _______
Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.
Example 5
f ( x)   x 4  6x3  x  9
Example 6
f ( x)  2x5  6x 4  x  4
Example 7
f ( x)  2x5  x 4  6x 2  8x
Example 8
f ( x)  2 x 2  6 x  6
Use the Graphs to analyze the Polynomial
Example 9
Example 10
Example 11
Example 12