Question 1147584
Find the quadratic 
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let the quadratic be Q(x) = Ax²+Bx+C
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which has a remainder of -6 when divided by x-1,

By the remainder theorem Q(1) = A(1)²+B(1)+C = 6
</pre>                                   A + B + C = 6
a remainder of -4 when divided by x-3, 
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By the remainder theorem Q(3) = A(3)²+B(3)+ C = 6
                                  9A + 3B + C = 6
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and no remainder when divided by x+1.
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By the remainder theorem Q(-1) = A(-1)²+B(-1)+C = 0
                                   A - B + C = 0
So solve this system of equations:

{{{system(A + B + C = 6,
9A + 3B + C = 6,
A - B + C = 0)}}}
The substitute the values you get for A,B, and C in

Q(x) = Ax²+Bx+C

and that'll be the answer.

Edwin</pre>