Moderate -0.8 This is a straightforward application of the factor and remainder theorems requiring students to set up two simultaneous equations (f(2)=0 and f(-1)=-6) and solve for a and b. It involves routine algebraic manipulation with no conceptual challenges or problem-solving insight needed, making it easier than average but not trivial since it requires careful arithmetic across multiple steps.
4 The cubic polynomial \(2 x ^ { 3 } - 5 x ^ { 2 } + a x + b\) is denoted by \(\mathrm { f } ( x )\). It is given that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x )\), and that when \(\mathrm { f } ( x )\) is divided by \(( x + 1 )\) the remainder is - 6 . Find the values of \(a\) and \(b\).
4 The cubic polynomial $2 x ^ { 3 } - 5 x ^ { 2 } + a x + b$ is denoted by $\mathrm { f } ( x )$. It is given that ( $x - 2$ ) is a factor of $\mathrm { f } ( x )$, and that when $\mathrm { f } ( x )$ is divided by $( x + 1 )$ the remainder is - 6 . Find the values of $a$ and $b$.
\hfill \mbox{\textit{CAIE P2 2004 Q4 [5]}}