Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2002  OctNov  (P29709/02)  Q#2
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Question
The polynomial is denoted by . It is given that is a factor of , and that when is divided by the remainder is 5. Find the values of and .
Solution
We are given that;
We are also given that is a factor of .
When a polynomial, , is divided by , and is factor of , then the remainder is ZERO i.e. .
We can write factor in standard form as;
Therefore;
We are also given that when is divided by the remainder is 5.
When a polynomial, , is divided by a , the remainder is the constant
We can write divisor in standard form as;
Therefore;
From we can substitute in above equation;
Substitution of in any of these two equations yields value of . We choose;
Hence;


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