OCR C1 — Question 5 7 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Identity Matching
DifficultyModerate -0.5 This is a straightforward polynomial expansion and coefficient matching problem. Students multiply out the left side, collect like terms, and equate coefficients with the right side to find three unknowns. It requires careful algebraic manipulation but no problem-solving insight—slightly easier than average for C1.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

  1. Given that
$$\left( x ^ { 2 } + 2 x - 3 \right) \left( 2 x ^ { 2 } + k x + 7 \right) \equiv 2 x ^ { 4 } + A x ^ { 3 } + A x ^ { 2 } + B x - 21 ,$$ find the values of the constants \(k , A\) and \(B\).

\begin{enumerate}
  \item Given that
\end{enumerate}

$$\left( x ^ { 2 } + 2 x - 3 \right) \left( 2 x ^ { 2 } + k x + 7 \right) \equiv 2 x ^ { 4 } + A x ^ { 3 } + A x ^ { 2 } + B x - 21 ,$$

find the values of the constants $k , A$ and $B$.\\

\hfill \mbox{\textit{OCR C1  Q5 [7]}}