11 The polynomial \(\mathrm { p } ( x )\) is given by
$$\mathrm { p } ( x ) = x ^ { 3 } + ( b + 2 ) x ^ { 2 } + 2 ( b + 2 ) x + 8$$
where \(b\) is a constant.
11
- Use the factor theorem to prove that \(( x + 2 )\) is a factor of \(\mathrm { p } ( x )\) for all values of \(b\).
11 - The graph of \(y = \mathrm { p } ( x )\) meets the \(x\)-axis at exactly two points.
11 - Sketch a possible graph of \(y = \mathrm { p } ( x )\)
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11
- (ii) Given \(\mathrm { p } ( x )\) can be written as
$$\mathrm { p } ( x ) = ( x + 2 ) \left( x ^ { 2 } + b x + 4 \right)$$
find the value of \(b\).
Fully justify your answer.