Question

When a polynomial f(x) is divided by (x-1) then the remainder is 5 and when it is divided by (x-2) then the remainder is 7. Find the remainder when it is divided by (x-1)(x-2).

Answer 1

Answer:

two equations remainder r(x) =2x+3

Step-by-step explanation:

Let us assume the polynomial to be f(x) .

When f(x) is divided by (x−1) , we get the remainder as 5 .

Therefore, f(1)=5

When f(x) is divided by (x−2) , we get the remainder as 7 .

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)=5

When, x=2

⇒f(2)=0.(x−1)q(2)+r(2)=7

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