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Answer

Suppose r(x) be the reminder when p(x) and q(x) is devided by (x-2). Then p(x)=(x-2)A(x)+r(x) and q(x)=(x-2)B(x)+r(x) implies p(x)-q(x)=(x-2)(A(x)-B(x)) implies p(2)-q(2)=o implies a=11.

Answer

Weight of alloy containing copper and zinc is 21kg and the ratio of copper to zinc is 5:2. Therefore weight of copper alloy contains is 5/7*21=15kg and weight of zinc alloy contains is 21-15=6kg. New weight of copper=15+4=19kg so new ratio is=19/6=19:6

Answer

New sequence is -2,0,2••••. So 8th term will be = -2+(8-1)*2=-2+14=12