# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | May-Jun | (P2-9709/02) | Q#3

Question

The cubic polynomial   is denoted by . It is given that  is a factor of .

i.       Find the value of .

ii.       When  has this value, solve the equation .

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. .

Therefore;

ii.

We are required to solve the equation;

We are given that;

Therefore;

We have found in (i) that , therefore;

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, division of with will yield a quadratic factor with ZERO remainder.

Therefore;

Hence;

Now we have two options.

One is a liner factor while other is quadratic factor and we need to solve both of them for

First we solve linear factor.