Polynomials & Factor Theorem (AQA GCSE Further Maths)

Use the factor theorem to show that  is a factor of .

Factorise  fully.

Use the factor theorem to show that is a factor of .

Hence solve  .

is a factor of   where is an integer.

Show that the value of is 1.

Hence, factorise fully   .

Solve

You must show your working.

The curve has an -intercept of .

Use this information to find the other two -intercepts.

where and are integers.

The equation has the solution and a different non-zero solution that is a repeated solution.

By factorising , or otherwise, find the values of and .

By first finding a factor of , show that the equation has one solution only.

where and are non-zero integers.

Work out .

Factorise fully, giving your answer in terms of and .