Moderate -0.8 This is a straightforward application of the division algorithm for polynomials: f(x) = (divisor)(quotient) + remainder. Students simply multiply out (x² + 1)(x² + 4x + 2) and add (x - 1), requiring only algebraic expansion with no problem-solving or conceptual insight.
1 When the polynomial \(\mathrm { f } ( x )\) is divided by \(x ^ { 2 } + 1\), the quotient is \(x ^ { 2 } + 4 x + 2\) and the remainder is \(x - 1\). Find \(\mathrm { f } ( x )\), simplifying your answer.
1 When the polynomial $\mathrm { f } ( x )$ is divided by $x ^ { 2 } + 1$, the quotient is $x ^ { 2 } + 4 x + 2$ and the remainder is $x - 1$. Find $\mathrm { f } ( x )$, simplifying your answer.
\hfill \mbox{\textit{OCR C4 2012 Q1 [3]}}