Answer:
k=3
Step-by-step explanation:
+ we note f(p)= [tex]p^{4}+p^{2} +p -k[/tex]
+ Because of "p-1 is a factor of f(p)", that means f(p)= (p-1)* g(p)
Then we have f(1)= (1-1)*g(1)= 0* g(1)= 0
+ We replace p=1 in f(p) and we have:
f(1)=0
that means: [tex]1^{4}+1^{2} + 1 - k=0[/tex]
then 1+1+1-k = 0, 3-k=0 or k=3
Hope that useful for you.
