Question

when a polynomial f(x) is divided by (x-1) ,the remainder ia 5 and when it is divided by (x-2),the remainder is 7 .find the remainder when it is divided by (x-1) (x-2)

Answer 1

We know that the remainder from (x-1) is 5
=> P(1) = 5

We know that the remainder from (x-2) is 7
=> P(2) = 7

We need to ánd out the remainder of polynomial P(x) when divided by (x-1)(x-2) Let us say D = (x-1)(x-2), the quotient is Q and the remainder is R

The remainder will be of the format Ax + B, because it is the remainder after division by a quadratic.
P(x) = Q*D + Ax + B

P(1) = Q*0 + A + B
=> 5 = A + B 

P(2) = Q*0 + 2A + B
=> 7 = 2A + B

Solving these equations, we get A =2 and B = 3 
=> R = Ax + B
=> Remainder is 2x + 3 

Answer 2

Answer:

Hope it will be helpful for you.