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^23x4 please tell me the way step by step to get the answer
4 when divided by x  3 and no remainder when divided by x + 1, the answers is x^23x4 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 ab+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
f(1)=6 so a+b+c=6
f(3)=4 so 9a+3b+c=4
f(1)=0 so ab+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