Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2017 | June | Q#3

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Question

The polynomial  is given by

.

where b and c are integers.

a.   Given that  is a factor of  show that .

b.   The remainder when  is divided by  is -30.

Obtain a further equation in b and c.

c.   Use equations from parts (a) and (b) to find the value of b and the value of c.

Solution

a.
 

Factor theorem states that if  is a factor of   then;

For the given case  is factor of .

We can write the divisor in standard form as;

Here  and . Hence;

b.
 

Remainder theorem states that if  is divided by  then;

For the given case   is divided by  and remainder is 65.

Here  and . Hence;

 

c.    

We are required to find values of b and c from equations obtained in parts (a) and (b).

These equations are;

Adding both equations;

Substituting  in any of the equations obtained in parts (a) and (b).

We choose;

Hence;

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