One unknown constant: find it then solve

3 The cubic polynomial \(2 x ^ { 3 } + a x ^ { 2 } - 13 x - 6\) is denoted by \(\mathrm { f } ( x )\). It is given that ( \(x - 3\) ) is a factor of \(\mathrm { f } ( x )\).

1. Find the value of \(a\).
2. When \(a\) has this value, solve the equation \(\mathrm { f } ( x ) = 0\).

3 The polynomial \(4 x ^ { 3 } - 7 x + a\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that ( \(2 x - 3\) ) is a factor of \(\mathrm { p } ( x )\).

1. Show that \(a = - 3\).
2. Hence, or otherwise, solve the equation \(\mathrm { p } ( x ) = 0\).

5 The polynomial \(3 x ^ { 3 } + 8 x ^ { 2 } + a x - 2\), where \(a\) is a constant, is denoted by \(\mathrm { p } ( x )\). It is given that \(( x + 2 )\) is a factor of \(\mathrm { p } ( x )\).

1. Find the value of \(a\).
2. When \(a\) has this value, solve the equation \(\mathrm { p } ( x ) = 0\).

2. $$f ( x ) = x ^ { 3 } + k x - 20 .$$ Given that \(\mathrm { f } ( x )\) is exactly divisible by ( \(x + 1\) ),

1. find the value of the constant \(k\),
2. solve the equation \(\mathrm { f } ( x ) = 0\).

$$f(x) = x^3 + kx - 20.$$ Given that f(x) is exactly divisible by \((x + 1)\),

1. find the value of the constant \(k\), [2]
2. solve the equation \(f(x) = 0\). [4]