Answer:
k = 3.
Step-by-step explanation:
If p-1 is a factor of the polynomial, that is
[tex]p^4+p^2+p-k = (p-1)q(p)[/tex]
with q(p) be another polynomial. Then with p=1 the polynomial is equal to 0. So,
[tex]1^4+1^2+1-k = 0[/tex]
[tex]1+1+1-k = 0[/tex]
[tex]3-k = 0[/tex]
[tex]k = 3[/tex].
