Distributive Property 100

1
Remainder/ Factor Theorem
End Behavior
Zeros / Graphs
Polynomials
Exponents
100
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100
200
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400
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500
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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

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)
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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?
• POLAND !
• Come on guys, that was the easiest 400 points in
  the game!

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10
Remainder/Factor Theorem 500
Determine if (x 2) is a factor of 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
No Calculator !
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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) (factor and set factors to
0 What about multiplicity?)
No Calculator !
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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?
• 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 / Graphs 100
Write a polynomial function of least degree
that has real coefficients, the given
zeros of 1, -1, -7 and a leading coefficient
of 1. Put the polynomial in standard form.
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23
Zeros / Graphs 100
Write a polynomial function of least degree
that has real coefficients, the given
zeros of 1, -1, -7 and a leading coefficient
of 1. Put the polynomial in standard form.
x3 7x2 x 7
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24
Zeros / Graphs 200
Find all of the possible rational zeros of
f (x) 3x5 2x4 7x2 9x 5
Main
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25
Zeros / Graphs 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 / Graphs 300
   
What are all the rational zeros of
f(x) x3 - 3x2 - 40x 84? (You
must prove it with synthetic division.)
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27
Zeros / Graphs 300
What are all the rational zeros of
f(x) x3 - 3x2 - 40x 84? (You
must prove it with synthetic division.)
Main
28
Zeros / Graphs 400
Use the graph to the right to answer the
following End Behavior As x ? ?,
f(x)?______________   As x ? -?,
f(x)?______________ Turning Points
_________________________ Degree of polynomial
_________________ You must give me the
coordinate (if any) in the following   Absolute
Min _______ Relative Min (Name one.)
__________ Absolute Max _______ Relative
Max (Name one.) _________
 
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29
Zeros / Graphs 400
Use the graph to the right to answer the
following End Behavior As x ? ?,
f(x)?______________   As x ? -?,
f(x)?______________ Turning Points
_________________________ Degree of polynomial
_________________ You must give me the
coordinate (if any) in the following   Absolute
Min _______ Relative Min (Name one.)
__________ Absolute Max _______ Relative
Max (Name one.) _________
-?
?
4
5
(-4,-5) or (-1,-2)
none
none
(-2, 4) or (1,4)
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30
Zeros / Graphs 500
What are all of the zeros of f(x) 2x3
11x2 8x 15
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31
Zeros / Graphs 500
What are all of the zeros of f(x) 2x3
11x2 8x 15
Graph to find that 5 is a zero. Synthetically
divide out the 5.
Use quadratic formula
2 -11 8 -15
5
2x2 x 3
10 -5 15
2 -1 3 0
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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
Create a polynomial with the following
characteristics quartic, leading
coefficient is 9, quadratic coefficient is 4,
linear coefficient is 5 and the constant term
is 2.
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35
Polynomials 200
Create a polynomial with the following
characteristics quartic, leading
coefficient is 9, quadratic coefficient is 4,
linear coefficient is 5 and the constant term
is 2.
9x4 4x2 5x 2
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36
Polynomials 300
If -6/11 is a zero of a polynomial function,
what is a factor?
Daily Double !
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37
Polynomials 300
If -6/11 is a zero of a polynomial function,
what is a factor?
(11x 6)
Daily Double !
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38
Polynomials 400
Find (-5x2 11x 1) (6x2 8x 7)
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39
Polynomials 400
Find (-5x2 11x 1) (6x2 8x 7)
-11x2 3x 6
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40
Polynomials 500
Factor 8x3 27
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41
Polynomials 500
Factor 8x3 27
(2x 3)(4x2 6x 9)
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42
Exponents100
Simplify.
(2y-5)(4x0)
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43
Exponents100
Simplify.
(2y-5)(4x0)
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44
Exponents200
Simplify.
(-2x3y-3)2
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45
Exponents200
Simplify.
(-2x3y-3)2
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46
Exponents300
Simplify.
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47
Exponents300
Simplify.
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48
Exponents400
Simplify.
(4x-2y)-2
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49
Exponents400
Simplify.
(4x-2y)-2
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50
Exponents500
Simplify.
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51
Exponents500
Simplify.
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