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Q1. When (x^3 – 2x^2 + px – q) is divided by (x^2 – 2x – 3), the remainder is (x – 6). Find the value of p and q.
Q2. If a,b,c are all non-zeroes and a+b+c=0, then find a^2/bc + b^2/ca + c^2/ab.
Q3. Find the remainder when the expression 3x^3 + 8x^2 – 6y + 1 is divided by x + 3.
Please ask your questions one at a time to receive answers. I will provide an answer to the first question. If you want answers to the others, ask them separately.
Q1) As shown in the attached figure, using long division, when
is divided by 
, the quotient is 
and the remainder is 
.
Given that the remainder is
, this means that 
and 
.
Therefore,
and 
.