Find the quadratic
let the quadratic be Q(x) = Ax²+Bx+C
which has a remainder of -6 when divided by x-1,
By the remainder theorem Q(1) = A(1)²+B(1)+C = 6
A + B + C = 6
a remainder of -4 when divided by x-3,
By the remainder theorem Q(3) = A(3)²+B(3)+ C = 6
9A + 3B + C = 6
and no remainder when divided by x+1.
By the remainder theorem Q(-1) = A(-1)²+B(-1)+C = 0
A - B + C = 0
So solve this system of equations:
The substitute the values you get for A,B, and C in
Q(x) = Ax²+Bx+C
and that'll be the answer.
Edwin