CAIE P3 2017 November — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Division by Quadratic Divisor
DifficultyModerate -0.8 This is a straightforward polynomial long division problem with a simple dividend (x^4) and a quadratic divisor. It requires only mechanical application of the division algorithm with no conceptual challenges or problem-solving insight, making it easier than average but not trivial since it involves a few steps and careful algebraic manipulation.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

Find the quotient and remainder when \(x^4\) is divided by \(x^2 + 2x - 1\). [3]

Question 1:
AnswerMarks Guidance
1Commence division and reach a partial quotient x2 +kx M1
Obtain quotient x2 −2x+5A1
Obtain remainder −12x+5A1
3
AnswerMarks Guidance
QuestionAnswer Marks
Question 1:
1 | Commence division and reach a partial quotient x2 +kx | M1
Obtain quotient x2 −2x+5 | A1
Obtain remainder −12x+5 | A1
3
Question | Answer | Marks
Find the quotient and remainder when $x^4$ is divided by $x^2 + 2x - 1$. [3]

\hfill \mbox{\textit{CAIE P3 2017 Q1 [3]}}