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Advanced Algebra D

Advanced Algebra D. Chapter 6 Review. Find the zeros and their multiplicity: f(x) = - 3x 6 - x 5 + 10x 4. 0 m4, 5/3 m1, 2 m1 0 m1, 5/3 m1, -2 m1 0 m4, 3 m1, -2 m1 0 m1, -3 m1, 2 m1 0 m4, -5/3 m1, 2 m1 0 m4, 5/3 m1, -2 m1 None of the above.

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Advanced Algebra D

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  1. Advanced Algebra D Chapter 6 Review

  2. Find the zeros and their multiplicity:f(x) = - 3x6- x5 + 10x4 • 0 m4, 5/3 m1, 2 m1 • 0 m1, 5/3 m1, -2 m1 • 0 m4, 3 m1, -2 m1 • 0 m1, -3 m1, 2 m1 • 0 m4, -5/3 m1, 2 m1 • 0 m4, 5/3 m1, -2 m1 • None of the above

  3. Find the end behavior: f(x) = - 3x6 - x5 + 10x4

  4. Determine the relative minimum(s) and relative maximum(s) f(x) = - 3x6 - x5 + 10x4 • Max: (-1.64, 25.84)Min: (0, 0) • Max: (1.36, 10.57)Min: (0,0) • Max: (-1.64, 25.84)Max: (1.36, 10.57) • None of the above Correct Answer:Max: (-1.64, 25.84) Max: (1.36, 10.57)Min: (0, 0)

  5. A zero with even multiplicity • Touches the x-axis and bounces away • Crosses the x-axis • Never hits the x-axis • Both 1 & 2 • None of the above

  6. A zero with odd multiplicity • Touches the x-axis and bounces away • Crosses the x-axis • Never hits the x-axis • Both 1 & 2 • None of the above

  7. Write a polynomial function in factored form with zeros 3 m1, -2 m2, 4/5 m1

  8. Write a polynomial function in STANDARD form with zeros 3 m1, -2 m2, 4/5 m1

  9. Solve for ALL solutions.0 = 27x3 + 125

  10. Solve for ALL solutions.0 = x4 – 14x2 + 45

  11. Solve for ALL solutions.0 = x3 + 2x2 - 2x - 4

  12. Find the quotient and remainder(x5 + x4 - 13x3 - 13x2 + 36x + 36) / (x2- 4)

  13. List all possible rational roots:f(x) = 6x3 + 5x2 - 3x + 15

  14. Find ALL zeros.f(x) = 2x4 - x3 + 7x2 - 5x - 15

  15. Write a polynomial function in factored form with zeros

  16. Box Problem • Advanced Algebra Students, Inc. is designing cardboard boxes without a top. The boxes will be made from a single sheet of cardboard where the corners will be cut out, then folded up to make a box.

  17. Box Problem • The company wants to maximize the volume of the box. To do so, you decide to write a function that would describe the total volume of the box given the length “x” of one side of the cutout.

  18. Box Problem • The company wants to maximize the volume of the box. To do so, you decide to write a function that would describe the total volume of the box given the length “x” of one side of the cutout.

  19. Box Problem • You are given the original sheet of cardboard is 12 inches X 20 inches

  20. Box Problem • You are given the original sheet of cardboard is 12 inches X 20 inches

  21. Box Problem • With your partner write a function to describe the volume “V(x)” based on the length of the cutout “x”

  22. Box Problem • V = L*W*H • H = x • L = 20 – 2x • W = 12 – 2x • V(x) = (20-2x)(12-2x)x

  23. Box Problem • Use your calculator to determine the maximum volume of the function • Coordinates of Relative Maximum:(2.43, 262.68) • Thus the maximum volume is 262.68 in3

  24. Box Problem • What would be the dimensions of the box that would produce that maximum volume? • H = 2.43 • L = 20-2(2.43) = 15.15 • W = 12-2(2.43) = 7.15 • 15.15in x 7.15in x 2.43in

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