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 Work2−−|220445813−626|20

Diane's Work2−−|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?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?