Let `a!=0a n dp(x)` be a polynomial of degree greater than 2. If `p(x)` leaves reminders `aa n d a` when divided respectively, by `+aa n dx-a ,` the remainder when `p(x)` is divided by `x^2-a^2` is `2x` b. `-2x` c. `x` d. ` x`

Explanation

According to the question P(-a) = and P(a) = - a. Let the remainder, when P(x) is divided by `x^(2)-a^(2)` be Ax + B. Then `P(x) = Q (x) (x^(2)-a^(2))` + Ax + B, where Q (x) is the quotient
Putting x = a, we get
P(a) = 0 + Aa + B
or Aa + B = - a ...(1)
Putting x = - a, we get
`-Aa + B = a` ...(2)
Solving (1) and (2) , we get
B = 0 and A = - 1
Hence, the requried remainder = Ax + B = - x