Question

An unknown polynomial is divided by x 1 to give a remainder 2 and with x 2 to give a remainder 1. Then the remainder resulting when the same polynomial is divided by (x 1)(x 2) is

Answer 1

Answer:

3-x

Step-by-step explanation:

Let f(x) = q1(x)*(x-1) + 2  -------------------(1)

and f(x) = q2(x)*(x-2) + 1 -----------------(2)

 Now, we multiply (1) by (x-2), and (2) by (x-1) we get

 (x-2)f(x) = q1(x)*(x-1)(x-2) + 2(x-2) ------------(3)

(x-1)f(x) = q2(x)*(x-2)(x-1) + 1(x-1) --------------(4)

 Subtracting (3) from(4)

 f(x)(x-1-x+2) =(x-1)(x-2)*[q2(x)-q1(x)]+x-1-2(x-2)

f(x)*(1)=(x-1)(x-2)*Q(x)+x-1-2x+4 [where Q(x)=q2(x)-q1(x)]

f(x)=(x-1)(x-2)*Q(x)-x+3

so the remainder= 3-x