Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2006  MayJun  (P29709/02)  Q#4
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Question
The cubic polynomial , where and are constants, is denoted by . It is given that and are factors of .
i. Find the values of and .
ii. When and have these values, find the other linear factor of .
Solution
i.
We are given that;
We are also given that and are a factors of .
When a polynomial, , is divided by , and is factor of , then the remainder is ZERO i.e. .
We can write the factors in standard form as;
Therefore;













We can substitute from into .
Substitution of in any of these two equations yields value of . We choose;
ii.
We are required to find other linear factor of .
We are given that;
We have found in (i) that and therefore;
We are also given that and are factors of . Therefore, division of with any of these factors will yield a quadratic factor with ZERO remainder.
We divide by by .
Therefore;
Hence, is another linear factor of .
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