Question

solve this yr please

Answer 1

Hello mate,

Let p(x) be the solution of the first division and q(x) be the solution of the second division.

Thus, 
f(x)= p(x). (x-1) + 2            f(x)= q(x). (x-2) + 1
                       .........(1)                              .......(2)

Multiplying (1) by (x-2) and (2) by (x-1),

f(x)(x-2) = p(x).(x-1).(x-2) + 2(x-2)   
f(x).(x-1) = q(x).(x-2).(x-1) + 1(x-1)

Subtracting the first of the new equations from the second gives you,

f(x) [(x-1) - (x-2)] = (x-1).(x-2) [q(x) - p(x)] + x - 1 - 2(x-2)
f(x) [(x-1 - x + 2] = (x-1).(x-2) [q(x) - p(x)] +x - 1 -2x + 4
f(x) [1] = (x-1).(x-2) [q(x)- p(x)] - x + 3
f(x) = (x-1).(x-2) [q(x) - p(x)] -x + 3

This equation is of the form, 
Dividend = Divisor x Quotient + Remainder.

Thus, when f(x) is divided by (x-1).(x-2), the remainder will be -x+3.

Hope this helps :)