Question

A polynomial P(x), whose degree is greater than 3, when divided with (x - 1) leaves a remainder 0. when divided by (x - 1)³ leaves a remainder x -1. Find the remainder when P(x) is divided by (x - 1)²​

Answer 1

Step-by-step explanation:

Given P(1)=3

P(3)=5

Let r(x)=ax+b

So P(x)=(x−1)(x−3)q(x)+ax+b

P(1)=a+b⇒ a+b=3

P(3)=3a+b⇒ 3a+b=5

a=1,b=2

r(x)=ax+b=x+2

r(−2)=(−2)+2)

r(−2)=0