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?