Partial Fractions (CIE A Level Maths: Pure 3)

Express    as partial fractions.

Write    in the form   , where and  are integers to be found.

It is given that

Show that .

Hence write down a factor of .

Show that

Hence write down another factor of .

Fully factorise .

Express    as partial fractions.

Express    as partial fractions.

Use algebraic division to work out .

Write   in the form 

Hence, or otherwise, show that

Express    as partial fractions.

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

Hence, or otherwise, fully factorise .

Show that   can be written in the form   , where and  are integers to be found.

Express    as partial fractions.

Express    as partial fractions.

Express    as partial fractions.

Express  as partial fractions.

Express    as partial fractions.

Write    in the form   , where and  are integers to be found.

It is given that

Show that 

Hence write down a factor of .

Fully factorise .

Express   as partial fractions.

Express    as partial fractions.

Show that    can be written in the form    , where  is an integer to be found.

Express   in the form    where and  are integers to be found.

Using your values for and  write   in the form 

Express    as partial fractions.

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

Hence, or otherwise, fully factorise .

Show that   can be written in the form   , where and  are integers to be found.

Express    as partial fractions.

Express    as partial fractions.

Express    as partial fractions.

Given that  fully factorise   where 

Hence express    as partial fractions.

Express    as partial fractions.

Write    in the form   , where and  are integers to be found.

Show that    can be written in the form   , where and  are integers to be found.

Express    as partial fractions.

Write    in the form   , where and  are integers to be found.

It is given that

Show that .

Hence, fully factorise  .

Express  as partial fractions.

Express    as partial fractions.

Express    as partial fractions.

Given that  , express  as partial fractions.

Express  as partial fractions.

Show that  

Express   as partial fractions.