Question

If f(x) is divided by (x-1) and (x+1) gives remainder 4, 8 respectively. The remainder when f(x) is divided by (x-1)(x+1) is

Answer 1

Answer:

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 

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