Edexcel C2 — Question 5 8 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks8
PaperDownload PDF ↗
TopicFactor & Remainder Theorem
TypeTwo unknowns, direct system
DifficultyModerate -0.8 This is a straightforward application of the Remainder Theorem requiring students to substitute values, set up two simultaneous equations, and solve for constants. Part (b) is routine verification by substitution. The question involves standard C2 techniques with no conceptual challenges or novel problem-solving required, making it easier than average.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

\(f(x) = x^3 - 2x^2 + ax + b\), where \(a\) and \(b\) are constants. When \(f(x)\) is divided by \((x - 2)\), the remainder is 1. When \(f(x)\) is divided by \((x + 1)\), the remainder is 28.
  1. Find the value of \(a\) and the value of \(b\). [6]
  2. Show that \((x - 3)\) is a factor of \(f(x)\). [2]

$f(x) = x^3 - 2x^2 + ax + b$, where $a$ and $b$ are constants.

When $f(x)$ is divided by $(x - 2)$, the remainder is 1.

When $f(x)$ is divided by $(x + 1)$, the remainder is 28.

\begin{enumerate}[label=(\alph*)]
\item Find the value of $a$ and the value of $b$.
[6]

\item Show that $(x - 3)$ is a factor of $f(x)$.
[2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2  Q5 [8]}}