Question

plz give answer show that p-1 is a factor of p^10-1 and also of p^11-1.

Answer 1

Given that p - 1 is a factor of p^(10) - 1.

By factor theorem, we get

= > p - 1 = 0

= > p = 1.


Plug x = 1, we get

= > (1)^(10) - 1

= > 1 - 1

= > 0.


Given that p - 1 is a factor of p^(11) - 1.

plug x = 1, we get

= > 1^(11) - 1

= > 1 - 1

= > 0.



Therefore (p - 1) is a factor of p^(10) - 1 and p^(11) - 1.


Hope this helps!

Answer 2

case 1
q(p)=p(raised to 10)-1
zero of p-1=0
p=1
q(1)=1(raised to 10)-1
1-1=0

case 2
q(p)=p(raised to 11)-1
zero of p-1=0
p=1
q(1)=1(raised to 11)-1
1-1=0
(hence proved that p-1 is a factor of p(raised to 10) and p(raised to 11) by remainder theorem)