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?

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

need more information

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!