Moderate -0.3 This is a straightforward application of the Remainder Theorem requiring two substitutions and solving a simple linear equation. While it involves connecting two polynomial divisions, the algebraic manipulation is routine and the problem structure is standard for C1 level, making it slightly easier than average.
7 The remainder when \(x ^ { 3 } - 2 x + 4\) is divided by ( \(x - 2\) ) is twice the remainder when \(x ^ { 2 } + x + k\) is divided by ( \(x + 1\) ).
Find the value of \(k\).
7 The remainder when $x ^ { 3 } - 2 x + 4$ is divided by ( $x - 2$ ) is twice the remainder when $x ^ { 2 } + x + k$ is divided by ( $x + 1$ ).\\
Find the value of $k$.
\hfill \mbox{\textit{OCR MEI C1 Q7 [5]}}