Polynomial quadratic equation help

Find the quadratic which has a remainder of -6 when divided by x - 1, a remainder of
-4 when divided by x - 3 and no remainder when divided by x + 1, the answers is x^2-3x-4 please tell me the way step by step to get the answer

f(x)=ax^2+bx+c
f(-1)=-6 so a+b+c=-6
f(3)=-4 so 9a+3b+c=-4
f(-1)=0 so a-b+c=0
From 1st and 3rd subtract and get 2b==-6 so b=-3
1st is now a+c=-3
2nd is 9a+c=5
Subtract to get 8a=8, so a=1
Substitute into a+c=3 to get c=-4