10.
$$g ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 41 x - 70$$
- Use the factor theorem to show that \(\mathrm { g } ( x )\) is divisible by \(( x - 5 )\).
- Hence, showing all your working, write \(\mathrm { g } ( x )\) as a product of three linear factors.
The finite region \(R\) is bounded by the curve with equation \(y = \mathrm { g } ( x )\) and the \(x\)-axis, and lies below the \(x\)-axis.
- Find, using algebraic integration, the exact value of the area of \(R\).