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10 June, 06:39

Two students, Claude and Diane, were asked to use synthetic division and the Remainder Theorem to find the value of f (2) given f (x) = 2x^3+5x-6. Their work is shown here.

Claude's Work 2--|220445813-626|20

Diane's Work 2--|220-4-45813-6-26|-32

Part A: Which student correctly used synthetic division to find f (2) ?

Part B: What is the value of f (2) ?

Part C: Is x-2 a factor of 2x3+5x-6? In other words, is x=2 a zero of f (x) ?

Part D: What are all the methods that can be used to find out if x-2 is a factor of 2x3+5x-6?

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Answers (1)
  1. 10 June, 07:57
    0
    Step-by-step explanation:

    Part A

    In applying the synthetic division, the polynomial would be fully expressed as

    2x³ + 0x² + 5x - 6

    The coefficients are 2, 0, 5 and - 6

    The working becomes

    2| 2 0 5 - 6

    4 8 16

    2 4 13 10

    The student that correctly used synthetic division to find f (2) is Claudia

    Part B

    The value of f (2) is

    2 (2) ^3+5 (2) - 6

    = (2 * 8) + 10 - 6

    = 16 + 10 - 6 = 20

    Part C

    x - 2 is not a factor of 2x³ + 5x - 6 because there is a remainder of 20.

    Part D

    The methods that can be used to find out if x - 2 is a factor of 2x³ + 5x - 6 are synthetic division, long division, remainder theorem
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