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2 years ago

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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?

1 answer:

ad-work [718]2 years ago

8 0

Answer:

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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ANSWER TO QUESTION 1

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ANSWER TO QUESTION 2

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{ $1,2,3,4,5,6,7,8,9,10$ }

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ANSWER TO QUESTION 3

The distance is given by the absolute value equation

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