1. 5.3 Polynomial Functions
By Willis Tang

2. Major Topics Describing end behaviors of polynomial functions
Finding real zeroes
Identifying degree and leading polynomials

3. The degree would be 3 and the leading coefficient would be 4.
Terms
Leading coefficient:The coefficient of the first term of the polynomial in standard form
Polynomial Function: continuous function that can be described by a polynomial equation in one variable
Polynomial equation in one variable: A polynomial equation with one variable
Degree: Highest exponent
Ex: 4x3+2x2+3x+5
The degree would be 3 and the leading coefficient would be 4.

4. Example 1: Describe the end behavior
Determine whether it represents an odd- degree or an even- degree polynomial function
State the number of real zeroes
Answer:
f(x) ∞ as x -∞, f(x) ∞ as x ∞
Even-degree function
4 real zeroes

5. Example 2: Describe the end behavior
Determine whether it represents an odd- degree or an even- degree polynomial function
State the number of real zeroes
Answer:
f(x) ∞ as x -∞, f(x) ∞ as x ∞
Odd-degree function
5 real zeroes

6. Find the leading coefficient and degree
Example 3:
Find the leading coefficient and degree
3x4+8x3+2x2+9x+5
Answer:
Leading Coefficient: 3
Degree: 4

7. Practice Problem #1 Describe the end behavior
Determine whether it represents an odd- degree or an even- degree polynomial function
State the number of real zeroes
Answer:
f(x) ∞ as x -∞, f(x) ∞ as x ∞
Odd-degree function
3 real zeroes

8. Practice Problem #2 Describe the end behavior
Determine whether it represents an odd- degree or an even- degree polynomial function
State the number of real zeroes
Answer:
f(x) ∞ as x -∞, f(x) ∞ as x ∞
Even-degree function
4 real zeroes ( one double root )

9. Find the leading coefficient and degree
Practice Problem #3
Find the leading coefficient and degree
5x5+6x4+x3+9x2+4x+10
Answer:
Leading Coefficient: 5
Degree: 5