If f(x)=x3+lx+m leaves the same reminder when divided by (x-1) or by (x+1). Find values of l and m?

Answer 1

do a little synthetic division.
R(x-1) = m+(l+1)
R(x+1) = m-(l+1)

m-(l+1) = m+(l+1)
2(l+1) = 0
l = -1

and m can be anything. So,

f(x) = x^3-x+m

the remainder is always m.