9709 P33 - Nov 2011 - Q7
1431
The polynomial \(p(x)\) is defined by
\(p(x) = ax^3 - x^2 + 4x - a\),
where \(a\) is a constant. It is given that \((2x - 1)\) is a factor of \(p(x)\).
Find the value of \(a\) and hence factorise \(p(x)\).
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