Which of the following is not a factors of 2p\(^2\) - 2?

Answer Details

To determine which of the options is not a factor of 2p\(^2\) - 2, we can factorize the expression first. We can start by taking out a common factor of 2:
2p\(^2\) - 2 = 2(p\(^2\) - 1)
We can then further factorize the expression inside the parentheses using the difference of squares:
2p\(^2\) - 2 = 2(p - 1)(p + 1)
Now we can check each of the options to see if they are factors of the expression.
- 2 is a factor since it is a common factor of the original expression.
- p - 1 is a factor since it is one of the factors obtained from the factorization.
- p + 1 is a factor since it is the other factor obtained from the factorization.
- 2p - 2 is a factor since it is equivalent to 2(p - 1).
- 2p + 1 is not a factor of the expression since it cannot be obtained by any combination of the factors we found earlier.
Therefore, the answer is 2p + 1.