Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | Oct-Nov | (P2-9709/02) | Q#4

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Question

The cubic polynomial  is denoted by . It is given that  is a factor of , and that when  is divided by  the remainder is -6. 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. .

Therefore;

We are also given that when is divided by the remainder is -6.

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;

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