Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2008 | Oct-Nov | (P2-9709/02) | Q#2

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Question

The polynomial , where a is a constant, is denoted by . It is given that is a factor of .


i.      
Find the value of  .

   ii.       When  has this value, factorise  completely.

Solution

     i.
 We are given that;

  

We are also given that is a factor of .

We can write the given factor in standard form as;

When a polynomial, , is divided by , and  is factor of , then the remainder is ZERO i.e. .

Therefore;

   ii.
 

We are required to factorise .

We are given that;

 

We have found in (i) that , therefore;

 

We are already given that  is a factor of .

When a polynomial, , is divided by , and  is factor of , then the remainder is ZERO i.e. .

Therefore, when is divided by factor , it will yield a quadratic factor with ZERO  remainder.

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Therefore;

 

 

 

 

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