Question

When polynomial f(x) is divided by (X-1) and (x - 2) it leaves remainder 5 and 7
respectively. What is the remainder when f(x) is divided by (x-1)(x-2).​

Answer 1

Answer:

When f(x)is divided by (x−1) we get the remainder as 55.

Therefore, f(1)=5

When f(x)is divided by (x−2) we get the remainder as 77.

Therefore, f(2)=7

Now, when same polynomial f(x)

is divided by (x−1)(x−2), the remainder is given by:

f(x)=q(x).(x−1)(x−2)+r(x)

When, x=1

⇒f(1)=0.(x−2)q(1)+r(1)

When, x=2x=2

⇒f(2)=0.(x−1)q(2)+r(2)=7

Solving above two equations, we get remainder r(x)=2x+3