12 The function \(\mathrm { f } ( x )\) is given by \(\mathrm { f } ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x - 12\).
- Show that \(( x + 3 )\) is a factor of \(\mathrm { f } ( x )\).
- Find the other factors of \(\mathrm { f } ( x )\).
- State the coordinates where the graph of \(y = \mathrm { f } ( x )\) cuts the \(x\) axis.
Hence sketch the graph of \(y = \mathrm { f } ( x )\).
- On the same graph sketch also \(y = x ( x - 1 ) ( x - 2 )\) Label the two points of intersection of the two curves A and B .
- By equating the two curves, show that the \(x\) coordinates of A and B satisfy the equation \(3 x ^ { 2 } + x - 4 = 0\).
Solve this equation to find the \(x\)-coordinates of A and B .