OCR C4 2005 June — Question 1 4 marks

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2005
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPolynomial Division & Manipulation
TypePolynomial Division by Quadratic Divisor
DifficultyModerate -0.8 This is a straightforward polynomial long division question requiring a standard algorithmic procedure with no conceptual difficulty. The division is clean with manageable coefficients, and at 4 marks it's a routine C4 exercise testing basic algebraic manipulation rather than problem-solving or insight.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

Find the quotient and the remainder when \(x^4 + 3x^3 + 5x^2 + 4x - 1\) is divided by \(x^2 + x + 1\). [4]

AnswerMarks Guidance
(Quotient) = \(x^2 + 2x + 2\)B1, M1, A1, A1 4 For correct leading term \(x^2\) in quotient; For evidence of division/identity process; For correct quotient; For correct remainder. The '0x' need not be written but must be clearly derived.
(Remainder) = \(0x - 3\) Allow without working
(Quotient) = $x^2 + 2x + 2$ | B1, M1, A1, A1 4 | For correct leading term $x^2$ in quotient; For evidence of division/identity process; For correct quotient; For correct remainder. The '0x' need not be written but must be clearly derived.

(Remainder) = $0x - 3$ | | Allow without working
Find the quotient and the remainder when $x^4 + 3x^3 + 5x^2 + 4x - 1$ is divided by $x^2 + x + 1$. [4]

\hfill \mbox{\textit{OCR C4 2005 Q1 [4]}}