When a polynomial f(x) is divided by x+1, the reminder is a. If f(2x+1) is divided by x+1, the reminder is...? (in terms of a)

@Callisto again haha sorry for that

Question

When a polynomial f(x) is divided by x+1, the reminder is a. If f(2x+1) is divided by x+1, the reminder is...? (in terms of a)

@Callisto again haha sorry for that

anonymous · Answer

is it a?
f[2(-1)+1]=f(-1)
same as f(x) ??

callisto · Answer

Hmmm... Not really.

anonymous · Answer

oh why?

callisto · Answer

Let me check something first...

anonymous · Answer

take you time xd

callisto · Answer

Haha!
f(x) is divided by x+1, the reminder is a.
=> f(x) = (x+1) Q(x) + a
Check: f(-1)  = a

 f(2x+1) = [(2x+1) + 1] Q(2x+1) +a
              = (2x+2) Q(2x+1) + a
              = 2(x+1) Q(2x+1) + a
So, f(-1) = ... XD
Haha, you're right XD

anonymous · Answer

haha i know more about polynomials now xD thank you!!!!

callisto · Answer

You're welcome!!!