Paper 2 October/November 2003 MATHEMATICH (9709/2) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

The polynomial $f\left( x \right)$ is defined by
$f\left( x \right) = 3{x^3} + \alpha {x^2} + \alpha x + \alpha $.
where $\alpha $ is a constant.
a) Given that $\left( {x + 2} \right)$ is a factor of $f\left( x \right)$, find the value of $\alpha $.
b) When $\alpha $ has the value found in part (a), find the quotient when $f\left( x \right)$ is divided by $\left( {x + 2} \right)$.