Question

Divide x+p+1 by p(p+1)​

Answer 1

Answer:

P(x) is non –zero polynomial and P(1+x)=P(1−x) for all x

Differentiate w.r.t x

P

′

(1+x)=−P

′

(1−x)

Put x=0,P

′

(1)=−P

′

(1)

⇒P

′

(1)+P

′

(1)=0

⇒2P

′

(1)=0

⇒P

′

(1)=0

and P(1)=0⇒P(x) touches the x− axis at x=1

⇒P(x)=(x−1)

2

Q(x)

⇒m=2 such that (x−1)

m

divides P(x) for all such P(x