4.
$$f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + 5 x + k \right) + 21$$
where \(k\) is a constant.
- State the remainder when \(\mathrm { f } ( x )\) is divided by ( \(x - 2\) )
Given that ( \(2 x - 1\) ) is a factor of \(\mathrm { f } ( x )\)
- show that \(k = 11\)
- Hence
- fully factorise \(\mathrm { f } ( x )\),
- find the number of real solutions of the equation
$$\mathrm { f } ( x ) = 0$$
giving a reason for your answer.