# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2005 | May-Jun | (P2-9709/02) | Q#5

Hits: 14

** Question**

The polynomial is denoted by . It is given that is a factor of and that when is divided by the remainder is 12.

** i. **Find the values of a and b.

** ii. **When and have these values, factorise .

**Solution**

** i.
**

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. .

We can write the factor in standard form as;

Therefore;

We are also given that when is divided by the remainder is 12.

When a polynomial, , is divided by a , the remainder is the constant

Therefore;

From we can substitute in above equation;

Substitution of in any of these two equations yields value of . We choose;

** ii.
**

We are required to factorise .

We are given that;

We have found in (i) that and therefore;

We are also given that is a factor of . Therefore, division of with will yield a quadratic factor with ZERO remainder.

Therefore;

## Comments