Rational Number Theorem

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8
• ±1, ±2, ±4, ±8
• ±1, ±2, ±4
• 1, 2, 4, 8

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

• ±1, ±7, ±1/3, ±7/3
• ±1, 7
• ±1, ±3, ±7, ±7/3
• ±1, ±3, ±7, ±1/3, ±7/3

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

• ±1, ±5, ±1/2, ±5/2
• ±1, ±2, ±5, ±1/2, ±5/2
• ±1, ±5
• ±1, ±2, ±5, ±1/2, ±5/2, ±2/5

Solve by using Rational Root Theorem: 
2x³ - 11x² + 12x + 9 = 0

• -1, 1, 3
• -1, 3/2, 3 
• -1/2, 3, 3
• -1/2, 1, 3

Solve by using Rational Root Theorem: 
x³ - 7x - 6 = 0

• 1, 2, 3
• -1, -2, - 3
• -1, -2, 3
• 1,-2,-3

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

• 3   0   -4   6   1
• 6   -4   3   1   0
• 6   -4   0   3   1
• -6   4   0   -3   -1

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0
• 2
• 4
• 6

            Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.
• No, (x-2) is  not a factor. The remainder is zero.
• Yes, (x-2) is a factor. The remainder is zero.
• No, (x-2) is  not a factor. There is a remainder. 

According to the Rational Root Theorem, what are the all possible rational roots? 
2x³ - 11x² + 12x + 9 = 0

• ±1,±2
• ±1,±3,±9
• ±1,±3±9,±1/2,±3/2,±9/2
• ±1,±2,±1/3,±2/3,±1/9,±2/9

Solve by using Rational Root Theorem: 
x³ + 3x² - 6x - 8 = 0

•  -4, -1, 2
• -4, -1, ±√2
• 1, 2, 4
• 4,-1,√2