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?

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