4 The polynomial \(\mathrm { p } ( x )\) is defined by
$$\mathrm { p } ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } + k x - 30$$
where \(k\) is a constant. It is given that \(( x - 3 )\) is a factor of \(\mathrm { p } ( x )\).
- Find the value of \(k\).
- Hence find the quotient when \(\mathrm { p } ( x )\) is divided by ( \(x - 3\) ) and factorise \(\mathrm { p } ( x )\) completely.
- It is given that \(a\) is one of the roots of the equation \(\mathrm { p } ( x ) = 0\).
Given also that the equation \(| 4 y - 5 | = a\) is satisfied by two real values of \(y\), find these two values of \(y\).