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200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Remainder/ Factor Theorem End Behavior Zeros PolynomialsGrab.

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Presentation on theme: "200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Remainder/ Factor Theorem End Behavior Zeros PolynomialsGrab."— Presentation transcript:

1 Remainder/ Factor Theorem End Behavior Zeros PolynomialsGrab Bag

2 Remainder/Factor Theorem 100 Main Get Answer Use the Remainder Theorem (Synthetic Substitution) to find f(3) for f(x) = 4x 4 – 2x 3 – 10x A. -10B. -60 C. 125D. 170

3 Use the Remainder Theorem to find f(3) for f(x) = 4x 4 – 2x 3 – 10x A. -10B. -60 C. 125D. 170 Main Remainder/Factor Theorem 100

4 Main Get Answer Divide 2x 3 + 5x 2 – 7x – 1 by (2x+3) HINT: Use long division Remainder/Factor Theorem 200

5 Main Remainder/Factor Theorem 200 Divide 2x 3 + 5x 2 – 7x – 1 by (2x+3) x 2 + x – 5 + _14__ (2x+3)

6 Remainder/Factor Theorem 300 Main Get Answer Divide 3x x x + 22 by (x+4)

7 Remainder/Factor Theorem 300 Main 3x 2 + 4x _2__ (x+4) Divide 3x x x + 22 by (x+4)

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? Main Get Answer

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, I’m not that vain ! Main

10 Remainder/Factor Theorem 500 Main Get Answer Determine if (x – 2) is a factor of: PROVE YES/NO w/ synthetic division f(x) = 4x 3 – 9x 2 – 3x + 12

11 Remainder/Factor Theorem 500 Main No, but you must prove it with synthetic division for your points! Determine if (x – 2) is a factor of: f(x) = 4x 3 – 9x 2 – 3x + 12

12 End Behavior 100 Main Get Answer Describe the end behavior of f(x) = -6x x 4 – 8x As x  +, f(x)  ______ As x  -, f(x)  ______

13 End Behavior 100 Main Describe the end behavior of f(x) = -6x x 4 – 8x As x  +, f(x)  ______ As x  -, f(x)  ______

14 End Behavior 200 Main Get Answer Describe the end behavior of f(x) = 6x x 3 – 8x + 11 As x  +, f(x)  ______ As x  -, f(x)  ______

15 End Behavior 200 Main Describe the end behavior of f(x) = 6x x 3 – 8x + 11 As x  +, f(x)  ______ As x  -, f(x)  ______

16 End Behavior 300 Main Get Answer Describe the end behavior of f(x) = -x x 3 – x As x  +, f(x)  ______ As x  -, f(x)  ______ Name one zero. ________

17 End Behavior 300 Main Describe the end behavior of f(x) = -x x 3 – x As x  +, f(x)  ______ As x  -, f(x)  ______ Name one zero. ________ x = 0

18 End Behavior 400 Main Get Answer Sketch the graph. How many turning points? What are the x-intercepts? f(x) = x 3 – 4x 2 + 4x

19 End Behavior 400 Main Sketch the graph. How many turning points? What are the x-intercepts? f(x) = x 3 – 4x 2 + 4x  (0, 0) and (2, 0)  Think about your ends.

20 End Behavior 500 Main Get Answer What is your favorite subject? a)Algebra 2 b) Algebra  c) Alg. 2 d) Math – specifically Algebra 2

21 End Behavior 500 Main Easy choice! Of course no other subject was even a contender! What is your favorite subject? (no calculator allowed for this ?) a)Algebra 2 b) Algebra 2 c) Alg. 2 d) Math – specifically Algebra 2

22 Zeros 100 Main Get Answer If a graph has 3 turning points, how many zeros will it have? _____________________________

23 Zeros 100 Main If a graph has 3 turning points, how many zeros will it have? _____________________________ 4

24 Zeros 200 Main Get Answer Find all of the possible rational zeros of: f (x) = 3x 5 + 2x 4 – 7x 2 – 9x + 5

25 Zeros 200 Main Find all of the possible rational zeros of: f (x) = 3x 5 + 2x 4 – 7x 2 – 9x + 5       

26 Zeros 300 Main Get Answer How many turning points does the following graph have? f (x) = x 3 – x – 2

27 Zeros 300 Main How many turning points does the following graph have? f (x) = x 3 – x – 2 2

28 Zeros 400 Main Get Answer How many real and imaginary zeros are there for the function: f (x) = x 3 + 3x 2 – 6x – 6

29 Zeros 400 Main How many real and imaginary zeros are there for the function: f (x) = x 3 + 3x 2 – 6x – 6 All three zeros are real.

30 Zeros 500 Main Get Answer How many real and imaginary roots are there for this function: f (x) = -4x x 3 + 3x 2 – 12x – 7

31 Zeros 500 Main How many real and imaginary roots are there for this function: f (x) = -4x x 3 + 3x 2 – 12x – 7 There are two real and two imaginary.

32 Polynomials 100 Main Get Answer At most, how many roots does the following polynomial have? f(x) = 5x 4 – 2x 3 + x 2 - 7

33 Polynomials 100 Main At most, how many roots does the following polynomial have? f(x) = 5x 4 – 2x 3 + x 

34 Polynomials 200 Main Get Answer Find the polynomial of least degree given the roots: 1, -1, 3, -3

35 Polynomials 200 Main Find the polynomial of least degree given the roots: 1, -1, 3, -3 (x 2 – 1)(x 2 – 9) = x 4 – 10x 2 + 9

36 Polynomials 300 Main Get Answer What is the complex conjugate of (3 + 7i)?

37 Polynomials 300 Main What is the complex conjugate of (3 + 7i)? (3 – 7i)

38 Polynomials 400 MainGet Answer Find the reduced polynomial of f(x) = x 3 – 4x 2 – 6x - 36 if (x – 6) is a known factor.

39 Polynomials 400 Main Find the reduced polynomial of f(x) = x 3 – 4x 2 – 6x - 36 if (x – 6) is a known factor. You must divide! Reduced polynomial is: (x 2 + 2x + 6)

40 Polynomials 500 MainGet Answer Solve and sketch f(x) = (x – 4)(x 2 – 3x – 4)

41 Polynomials 500 Main Solve and sketch f(x) = (x – 4)(x 2 – 3x – 4) f (x) = (x-4)(x-4)(x+1) = (x-4) 2 (x+1) x = 4, -1

42 Grab Bag 100 MainGet Answer Simplify the expression:

43 Grab Bag 100 Main Simplify the expression:

44 Grab Bag 200 Main Get Answer What is the simplified form of :

45 Grab Bag 200 Main What is the simplified form of :

46 Grab Bag 300 Main Get Answer Simplify the following expression:

47 Grab Bag 300 Main Simplify the following expression:

48 Grab Bag 400 Main Get Answer Decide whether or not the functions below are polynomials. You must have an explanation as to why your answer is such.

49 Grab Bag 400 Main 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)

50 Grab Bag 500 Main Get Answer Factor completely:

51 Grab Bag 500 Main Factor completely:


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