Moderate -0.8 This is a straightforward application of the factor and remainder theorems requiring two substitutions to form simultaneous equations. The arithmetic is routine (substituting x = -1/2 and x = -2), and solving the resulting linear system is standard. Below average difficulty as it's a direct textbook-style exercise with no conceptual challenges.
2 The polynomial \(6 x ^ { 3 } + a x ^ { 2 } + b x - 2\), where \(a\) and \(b\) are constants, is denoted by \(\mathrm { p } ( x )\). It is given that \(( 2 x + 1 )\) is a factor of \(\mathrm { p } ( x )\) and that when \(\mathrm { p } ( x )\) is divided by \(( x + 2 )\) the remainder is - 24 . Find the values of \(a\) and \(b\).
2 The polynomial $6 x ^ { 3 } + a x ^ { 2 } + b x - 2$, where $a$ and $b$ are constants, is denoted by $\mathrm { p } ( x )$. It is given that $( 2 x + 1 )$ is a factor of $\mathrm { p } ( x )$ and that when $\mathrm { p } ( x )$ is divided by $( x + 2 )$ the remainder is - 24 . Find the values of $a$ and $b$.\\
\hfill \mbox{\textit{CAIE P3 2019 Q2 [5]}}