OCR C2 — Question 1 4 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFactor & Remainder Theorem
TypeRemainder condition then further work
DifficultyModerate -0.8 This is a straightforward application of the Remainder Theorem requiring direct substitution and basic algebra. Part (i) involves substituting x=-2 and solving a linear equation for k, while part (ii) requires substituting x=2/3 into the polynomial. Both parts are routine C2-level exercises with no problem-solving insight needed, making this easier than average.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

  1. \(f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + k x + 9\).
Given that when \(\mathrm { f } ( x )\) is divided by \(( x + 2 )\) there is a remainder of - 35 ,
  1. find the value of the constant \(k\),
  2. find the remainder when \(\mathrm { f } ( x )\) is divided by \(( 3 x - 2 )\).

\begin{enumerate}
  \item $f ( x ) = 3 x ^ { 3 } - 2 x ^ { 2 } + k x + 9$.
\end{enumerate}

Given that when $\mathrm { f } ( x )$ is divided by $( x + 2 )$ there is a remainder of - 35 ,\\
(i) find the value of the constant $k$,\\
(ii) find the remainder when $\mathrm { f } ( x )$ is divided by $( 3 x - 2 )$.\\

\hfill \mbox{\textit{OCR C2  Q1 [4]}}