November 29, 2016
DO NOW!
1) Take back your graded homework.
3) Sit quietly to facilitate a rapid start to class
The Thanksgiving Blues....
2) Take out last night's homework and raise your hand for a stamp
November 29, 2016
Today's Agenda:1) Correct 6.5
2) 6.6: Finding Rational Zeros
3) 6.6(Ext): Descartes' Rule of Signs
Ch. 6 Test
November 29, 2016
Questions from last night's homework?
November 29, 2016
November 29, 2016
Review from yesterday:• Is (x+2) a zero of ?
How do we know?
November 29, 2016
6.6: Date:
• I CAN find all zeros of a polynomial function
November 29, 2016
Two Important Theorems:
Factor Theorem:
Let f be a polynomial function. Then (x-c) is a factor of f(x) if and only if f(c)=0.
Theorem - Number of Zeros:
Corollary: A polynomial function may have fewer real zeros than its degree.
A polynomial function has exactly as many zeros as its degree.
November 29, 2016
Determining Possible Zeros:
Find all Real Zeros:
Where do we start?
Rational Zeros TheoremFor a polynomial function, the possible rational zeros can be found by writing all ratios
where p is a factor of the constant term (last term)and q is a factor of the leading coefficient.
List possible zeros of f(x):
November 29, 2016
Your turn: Determining Possible Zeros:
List all possible Zeros:
November 29, 2016
At your table:
Find all Real Zeros:Steps:
Check your answer by graphing!
November 29, 2016
Your chance to learn more about your classmates!
Who is __________?We will ask question until the timer ends. Be creative!
Ground Rules:- Inappropriate questions will end the activity. Act responsibly so we can all enjoy the opportunity to get to know each other!
VIPSpotlight
November 29, 2016
Can we make this any easier? Yes!!• Descartes' Rule of Signs:
The number of positive real zeros of f(x) equals the number of sign changes in the coefficients of f(x) OR that number minus an even integer.
The number of negative real zeros of f(x) equals the number of sign changes in the coefficients of f(-x) OR that number minus an even integer.
November 29, 2016
Let's apply Descartes' Rule of Signs!
List all possible zero combinations:
November 29, 2016
Putting it all together: Question revisited:Find all Real Zeros:Steps:
November 29, 2016
Homework Time!• You may work alone or with the other members of
your table• Use your time Productively!
November 29, 2016
Concept Check:
Today we learned....
1) How to find all zeros of a polynomial
2) How to use Descartes' Rule of Signs to determine possible zeros of a polynomial
Update Your Assignment Sheet with Tonight's Homework:
Section 6.6 Assignment
Descarte's Rule of Signs Worksheet
Assigned: __________ Stamped: _________ Due: __________
