Problem: When y2+my+2 is divided by y−1 the quotient is f(y) and the remainder is R1. When y2+my+2 is divided by y+1 the quotient is g(y) and the remainder is R2. If R1=R2 then m is:
Answer Choices:
A. 0
B. 1
C. 2
D. −1
E. an undetermined constant
Solution:
Since y2+my+2=(y−1)f(y)+R1 is true for all values of y, we have, letting y=1,3+m=R1. Similarly, since y2+my+2=(y+1)g(y)+R2 is true for all values of y, we have, letting y=−1, 3−m=R2. Since R1=R2,3+m=3−m.∴m=0.