Question

Which of the following properly uses a polynomial identity to detect if  22k−1  is prime?(1 point)
Responses

22k−1=(2k+1)(2k−1), so 22k−1 is prime.
  2 superscript 2 k baseline minus 1 equals left parenthesis 2 superscript k baseline plus 1 right parenthesis left parenthesis 2 superscript k baseline minus 1 right parenthesis , so  2 superscript 2 k baseline minus 1  is prime.

22k−1=(2k+1)(2k−1), so 22k−1 is not prime.
2 superscript 2 k baseline minus 1 equals left parenthesis 2 superscript k baseline plus 1 right parenthesis left parenthesis 2 superscript k baseline minus 1 right parenthesis , so  2 superscript 2 k baseline minus 1  is not prime.

22k−1=(22+1)(2k−1), so 22k−1 is prime.
  2 superscript 2 k baseline minus 1 equals left parenthesis 2 superscript 2 baseline plus 1 right parenthesis left parenthesis 2 superscript k baseline minus 1 right parenthesis , so  2 superscript 2 k baseline minus 1  is prime.

22k−1=(22+1)(2k−1), so 22k−1 is not prime.

Answer 1

22k−1=(2k+1)(2k−1), so 22k−1 is not prime.