Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | Q#3

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Question

The polynomial  is denoted by p(x).


i.       
Find the quotient when p(x) is divided by  .

 ii.       Hence solve the equation  p(x)=0.

Solution

     i.
 

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Hence quotient is and remainder is .

 

   ii.
 

We are required to solve;

When a polynomial, , is divided by a non-constant divisor, , the quotient and the remainder  are defined by the identity;

As demonstrated in (i);

Since we are looking for solution of;

Therefore;

Now we have three options.

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