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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 Bag

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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 2 - 10 A. -10B. -60 C. 125D. 170

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

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

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

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Remainder/Factor Theorem 300 Main Get Answer Divide 3x 3 + 16x 2 + 21x + 22 by (x+4)

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Remainder/Factor Theorem 300 Main 3x 2 + 4x + 5 + _2__ (x+4) Divide 3x 3 + 16x 2 + 21x + 22 by (x+4)

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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

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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

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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

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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

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End Behavior 100 Main Get Answer Describe the end behavior of f(x) = -6x 17 + 5x 4 – 8x 2 + 10 As x +, f(x) ______ As x -, f(x) ______

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End Behavior 100 Main Describe the end behavior of f(x) = -6x 17 + 5x 4 – 8x 2 + 10 As x +, f(x) ______ As x -, f(x) ______

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End Behavior 200 Main Get Answer Describe the end behavior of f(x) = 6x 38 + 5x 3 – 8x + 11 As x +, f(x) ______ As x -, f(x) ______

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End Behavior 200 Main Describe the end behavior of f(x) = 6x 38 + 5x 3 – 8x + 11 As x +, f(x) ______ As x -, f(x) ______

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End Behavior 300 Main Get Answer Describe the end behavior of f(x) = -x 156 + x 3 – x As x +, f(x) ______ As x -, f(x) ______ Name one zero. ________

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End Behavior 300 Main Describe the end behavior of f(x) = -x 156 + x 3 – x As x +, f(x) ______ As x -, f(x) ______ Name one zero. ________ x = 0

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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

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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.

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

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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

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

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

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

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

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

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

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

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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.

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

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

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

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

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

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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

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

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

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

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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)

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

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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

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Grab Bag 100 MainGet Answer Simplify the expression:

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Grab Bag 100 Main Simplify the expression:

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

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Grab Bag 200 Main What is the simplified form of :

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Grab Bag 300 Main Get Answer Simplify the following expression:

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Grab Bag 300 Main Simplify the following expression:

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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.

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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)

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Grab Bag 500 Main Get Answer Factor completely:

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Grab Bag 500 Main Factor completely:

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Academy Algebra II/Trig 5.5: The Real Zeros of a Polynomial Functions HW: p.387 (14, 27, 30, 31, 37, 38, 46, 51)

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