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?

what do you mean by fog

step-by-step explanation:

true !

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1