4. Let \(f ( x )\) be given by: $$f ( x ) = x ^ { 3 } + x ^ { 2 } - 12 x - 18$$ a) Use the factor theorem to show that ( \(x + 3\) ) is a factor of \(f ( x )\)
b) Factorise \(f ( x )\) into a linear and a quadratic factor and hence find exact values for all of the solutions of the equation \(f ( x ) = 0\), showing detailed reasoning with your working
c) Hence write down the one solution to the equation $$e ^ { 3 x } + e ^ { 2 x } - 12 e ^ { x } - 18 = 0$$ in the form \(\ln ( a + \sqrt { b } )\)
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