# 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.

Therefore;

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