# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2003 | Oct-Nov | (P2-9709/02) | Q#3

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**Question**

The polynomial is denoted by .

** i. **It is given that

** ii. **When

**Solution**

**i. **

We are given that;

We are also given that

When a polynomial,

We can write factor in standard form as;

Therefore;

** ii.
**

We are required to verify that

We are given that;

We have found in (i) that

When a polynomial,

Therefore;

Hence

Therefore, now we have two factors of

A (non-zero) polynomial,

Where

Number

It is evident that

factors.

We can obtain one of the quadratic factors by multiplication of already obtained 02 linear factors.

Hence, we have quadratic factor of

When a polynomial,

Therefore, if we divide of

Therefore;

The second quadratic factor

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