Find the remainder when x^13 + 1 is divided by x - 1. Please explain!

Question

brinazarski · Answer

If it matters, I haven't done this stuff in awhile >.<

parthkohli · Answer

When $p(x)$ is divided by $x - k$, then the remainder is $p(k)$.

parthkohli · Answer

Here, just find $1^{13} + 1$

brinazarski · Answer

... 2?

anonymous · Answer

here u have to use factor and remainder theorem
let f(x) =x^13 +1  if it is divided by x-1 then 

x^13 +1= (x-1)Q(x) +R(x) 
 hence putting both sides x=1 
we have R(1) =1^13+1 =2
 hence the remainder is 2 when

anonymous · Answer

as the term  (x-1)Q(x) vanishes when x=1

brinazarski · Answer

I'm confused... not good with math. But the "p(x) is divided by x−k, then the remainder is p(k)." applies to all situations, right? Cuz I'll just jot that down for my own notes....

anonymous · Answer

yups

anonymous · Answer

see F(x)=(x-a)Q(x) +R(x) where Q(x) is the quotient and R(x) is the remainder thus if u put x=a then 
 F(xa=(a-a)Q(a) +R(a) hence R(a) =F(a)  and hence it applies to all situations

brinazarski · Answer

Ah... sort of makes sense. Thank you! :)

anonymous · Answer

welcome