Distributive Property 100

1
Remainder/ Factor Theorem
End Behavior
Zeros
Polynomials
Grab Bag
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Remainder/Factor Theorem 100

• Use the Remainder Theorem (Synthetic
  Substitution) to find f(3)
• for f(x) 4x4 2x3 10x2 - 10
• A. -10 B. -60
• C. 125 D. 170

Get Answer
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3
Remainder/Factor Theorem 100

• Use the Remainder Theorem to find f(3)
• for f(x) 4x4 2x3 10x2 - 10
• A. -10 B. -60
• C. 125 D. 170

Main
4
Remainder/Factor Theorem 200
Divide 2x3 5x2 7x 1 by (2x3) HINT
Use long division
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5
Remainder/Factor Theorem 200
Divide 2x3 5x2 7x 1 by (2x3)
x2 x 5 _14__ (2x3)
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6
Remainder/Factor Theorem 300
Divide 3x3 16x2 21x 22 by (x4)
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7
Remainder/Factor Theorem 300
Divide 3x3 16x2 21x 22 by (x4)
3x2 4x 5 _2__
(x4)
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8
Remainder/Factor Theorem 400

• If I were to look in the dictionary under the
  words greatest and math teacher, whose name
  would I see?

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9
Remainder/Factor Theorem 400

• If I were to look in the dictionary under the
  words greatest and math teacher, whose name
  would I see?
• Come on guys, Im not that vain? !

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10
Remainder/Factor Theorem 500
Determine if (x 2) is a factor of PROVE YES/NO
w/ synthetic division f(x) 4x3 9x2 3x
12
Get Answer
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11
Remainder/Factor Theorem 500
Determine if (x 2) is a factor of f(x)
4x3 9x2 3x 12
No, but you must prove it with synthetic division
for your points!
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12
End Behavior 100
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13
End Behavior 100
Describe the end behavior of f(x) -6x17
5x4 8x2 10 As x ? , f(x) ?
______ As x ? - , f(x) ? ______
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14
End Behavior 200
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15
End Behavior 200
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16
End Behavior 300
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17
End Behavior 300
x 0
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18
End Behavior 400
Sketch the graph. How many turning points? What
are the x-intercepts? f(x) x3 4x2 4x
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19
End Behavior 400
Sketch the graph. How many turning points? What
are the x-intercepts? f(x) x3 4x2 4x
Think about your ends.
2
(0, 0) and (2, 0)
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20
End Behavior 500

• What is your favorite subject?
• Algebra 2 b) Algebra 2
• c) Alg. 2 d) Math
• specifically Algebra 2

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21
End Behavior 500

• What is your favorite subject? (no calculator
  allowed for this ?)
• Algebra 2 b) Algebra 2
• c) Alg. 2 d) Math
• specifically Algebra 2

Easy choice! Of course no other subject was even
a contender!
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22
Zeros 100
If a graph has 3 turning points, how many zeros
will it have? _____________________________

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23
Zeros 100
If a graph has 3 turning points, how many zeros
will it have? _____________________________
4
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24
Zeros 200
Find all of the possible rational zeros of
f (x) 3x5 2x4 7x2 9x 5
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25
Zeros 200
Find all of the possible rational zeros of
f (x) 3x5 2x4 7x2 9x 5
1, 5


5,
1,
,
1, 3
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26
Zeros 300
   
How many turning points does the following graph
have? f (x) x3 x 2
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27
Zeros 300
How many turning points does the following graph
have? f (x) x3 x 2
2
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28
Zeros 400
How many real and imaginary zeros are there for
the function f (x) x3 3x2
6x 6
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29
Zeros 400
How many real and imaginary zeros are there for
the function f (x) x3 3x2
6x 6
All three zeros are real.
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30
Zeros 500
How many real and imaginary roots are there for
this function f (x) -4x4
12x3 3x2 12x 7
Main
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31
Zeros 500
How many real and imaginary roots are there for
this function f (x) -4x4
12x3 3x2 12x 7
There are two real and two imaginary.
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32
Polynomials 100
At most, how many roots does the following
polynomial have? f(x) 5x4
2x3 x2 - 7
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33
Polynomials 100
At most, how many roots does the following
polynomial have? f(x) 5x4
2x3 x2 - 7
4
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34
Polynomials 200
Find the polynomial of least degree given
the roots 1, -1, 3, -3
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35
Polynomials 200
Find the polynomial of least degree given
the roots 1, -1, 3, -3
(x2 1)(x2 9) x4 10x2 9
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36
Polynomials 300
What is the complex conjugate of (3 7i)?
Daily Double !
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37
Polynomials 300
What is the complex conjugate of (3 7i)?
(3 7i)
Daily Double !
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38
Polynomials 400
Find the reduced polynomial of f(x) x3 4x2
6x - 36 if (x 6) is a known factor.
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39
Polynomials 400
Find the reduced polynomial of f(x) x3 4x2
6x - 36 if (x 6) is a known factor.
You must divide! Reduced polynomial is (x2
2x 6)
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40
Polynomials 500
Solve and sketch f(x) (x 4)(x2 3x 4)
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41
Polynomials 500
Solve and sketch f(x) (x 4)(x2 3x 4)
f (x) (x-4)(x-4)(x1) (x-4)2(x1)
x 4, -1
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42
Grab Bag100
Simplify the expression
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43
Grab Bag100
Simplify the expression
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44
Grab Bag200
What is the simplified form of
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45
Grab Bag200
What is the simplified form of
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46
Grab Bag300
Simplify the following expression
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47
Grab Bag300
Simplify the following expression
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48
Grab Bag400
Decide whether or not the functions below are
polynomials. You must have an explanation as to
why your answer is such.
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49
Grab Bag400
Decide whether or not the functions below are
polynomials. You must have an explanation as to
why your answer is such.
f(x) yes g(x) - no (power of x)
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50
Grab Bag500
Factor completely
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51
Grab Bag500
Factor completely
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