Paper 3 October/November 2007 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 $\alpha {x^3} + b{x^2} + 5x - 2$, where $\alpha $ and $b$ are constants, is denoted by $p\left( x \right)$. It is given that $\left( {2x - 1} \right)$ is a factor of $p\left( x \right)$ and that when $p\left( x \right)$ is divided by $\left( {x - 2} \right)$ the remainder is 12.
a) Find the values of $\alpha $ and $b$.
b) When $\alpha $ and $b$ have these values, find the quadratic factor of $p\left( x \right)$.