1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

When a polynomial f (x) is divided by (x-1),the remainder is 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).

Open in App
Solution

Given when a polynomial f(x) is divided by x – 1 and x – 2, the remainders are 5 and 7 respectively. So, We get f(x) = (x - 1) q (x) + 5 We substitute x = 1, we get f(1) = (1 - 1)q (x) + 5 f(1) = 5 And f(x) = (x - 2)Q(x) + 7 We substitute x = 2, get f(2) = 2 (2 - 2) Q (x) + 7 f(2) = 7 Now Let the remainder Ax + B When f(x) divide by (x-1) (x-2), So f(x) = (x -1) (x -2)p (x) + Ax + B ------(A) We subtistute x = 1, we f(1) = (1 - 1) (1 - 2) p (x) + A(1) + B f(1) = 0 + A + B, Substitute value of f (1) we get A + B = 5 ----(1) And we substitute x = 2 in equation A, we get f(2) = (2 - 1) (2 - 2) p(x) + A(2) + B f(2) = 0 + 2A + B, Substitute value of f (2) we get 2A + B = 7 ----(2) Now we substract equation 1 from equation 2, we get A = 2, Substitute that value in equation 1, we get 2 + B = 5 B = 3 So, Remainder = Ax + B = (2) x + 3 = 2x + 3

Suggest Corrections
13
Join BYJU'S Learning Program
Related Videos
Remainder Theorem
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program