| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2026 |
| Session | November |
| Marks | 7 |
| Topic | Factor & Remainder Theorem |
| Type | Known polynomial, verify then factorise |
| Difficulty | Easy -1.2 This is a straightforward multi-part question on polynomial factorisation using the factor theorem. Part (a) requires simple substitution to verify a given factor, part (b) involves routine polynomial division and factorising a quadratic, and part (c) is direct reading of roots from the factorised form. All steps are standard textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$f(x) = x^3 + 4x^2 + x - 6$.
\begin{enumerate}[label=(\alph*)]
\item Use the factor theorem to show that $(x + 2)$ is a factor of $f(x)$.
[2]
\item Factorise $f(x)$ completely.
[4]
\item Write down all the solutions to the equation
$$x^3 + 4x^2 + x - 6 = 0.$$
[1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2026 Q2 [7]}}