Given that the polynomial (x2+ ax+ b) leaves that same remainder when by (x ?1) or (x + 1) What are the values of a and b respectively?

Since x^2+ ax + b when divided by x-1 or x+1 leaves the same remainder

So on putting x=1 and x=-1 we get the same value

1+a+b = 1-a+b

2a=0

a=0

here b can take any value as it will always get cancelled out