Paper 3 May/June 2003 MATHEMATICH (9709/3) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

The polynomial $p\left( x \right)$ is defined by
$p\left( x \right) = \alpha {x^3} - {x^2} + 4x - \alpha $
where a is $\alpha $ constant. It is given that $\left( {2x - 1} \right)$ is a factor of $p\left( x \right)$.
a) Find the value of $\alpha $ and hence factorise $p\left( x \right)$.
b) When $\alpha $ has the value found in part (a), express $\frac{{8x - 13}}{{p\left( x \right)}}$ in partial fractions.