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 $\alpha {x^3} - 3{x^2} - 11x + b$, where $\alpha $ and $b$ are constants, is denoted by $p\left( x \right)$. It is given that $\left( {x + 2} \right)$ is a factor of $p\left( x \right)$, and that when $p\left( x \right)$ is divided by $\left( {x + 1} \right)$ the remainder is 12.
a) Find the values of $\alpha $ and $b$.
b) When $\alpha $ and $b$ have these values, factorise $p\left( x \right)$ completely.