plumiPolynomials and the factor theorem: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 2.6 Polynomials and the factor theorem, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
All papers
All years
Loading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDFLoading the question…
Open the full PDF
All 15 questions on Polynomials and the factor theorem, as a list
- June 2025, Paper 2, Q4 (5 marks): 2 4 (a) Use the factor theorem to show that ( x 3 ) is a factor of x 4 8 x 11 x - . 3 [1] - - - 3 2 2 (b) Hence show that 4 x 8 x 11 x 3 ( x 3 )( ax b ) , where
- June 2025, AS Paper 1, Q11 (9 marks): In this question you must show detailed reasoning. 2 f x x x x You are given that ( ) ( 2 )( 7 6 ) . = + - + (a) Solve the equation ( ) f x [3] 0 . = (b) Show t
- June 2024, Paper 3, Q16 (2 marks): x x x x x x c m c m c m is equivalent to + + - P Q P Q P Q 16 Show that the expression a b c a + + - 2 2 2 x x c m + P Q ax x b c , as given in lines 15 and 16.
- June 2024, AS Paper 1, Q6 (6 marks): 2 6 The polynomial x 4 x 10 x 21 is denoted by ( )x f . - + - (a) Use the factor theorem to show that ( x 3 ) is a factor of ( )x f . [2] - 2 (b) The polynomial
- June 2024, AS Paper 2, Q1 (3 marks): + 2 1 Express 2 x x ( 3 ) 5 x 2 ( x 3 ) in the form ax bx + , where a, b and c are integers to be c + + - - determined. [3]
- June 2023, Paper 3, Q4 (4 marks): In this question you must show detailed reasoning. 3 2 Find the coordinates of the points where the curve y x 2 x 5 x + crosses the x‑axis. 6 [4] = - -
- June 2023, AS Paper 1, Q6 (5 marks): 2 2 6 Show that the expression x 3 x 6 x - can be written in the form ( 5 x 2 )( ax bx c ) + d + - + + + where a, b, c and d are constants to be determined. [5]
- June 2023, AS Paper 2, Q7 (4 marks): 2 7 (a) Use the factor theorem to show that ( x 2 ) is a factor of x 6 x x 30 . [1] - + - - 3 2 (b) Factorise x 6 x x 30 completely. [3] + - -
- June 2022, AS Paper 2, Q10 (9 marks): In this question you must show detailed reasoning. 3 2 The equation of a curve is y 12 x 24 x 60 x 72 . = - - + Determine the magnitude of the total area bounde
- November 2021, AS Paper 2, Q13 (9 marks): In this question you must show detailed reasoning. 7 3 The equation of a curve is y 3 x . = + - x 2 x Determine the coordinates of the points on the curve where
- November 2020, Paper 1, Q7 (6 marks): In this question you must show detailed reasoning. 3 2 The function ( )x f is defined by ( )x f x x 8 x 12 for all values of x. = + - - (a) Use the factor theor
- November 2020, AS Paper 2, Q6 (6 marks): Use integration to show that the area bounded by the x-axis and the curve with equation 4 square units. 2 y ( x 1 ) ( x 3 ) is 3 [6] = - -
- June 2019, AS Paper 1, Q7 (11 marks): In this question you must show detailed reasoning. 3 - (a) Nigel is asked to determine whether ( x 7 ) is a factor of x 37 x 84 . He substitutes x 7 + + = 3 and
- June 2018, Paper 1, Q1 (3 marks): 2 1 x is a factor of x x x [3] Show that ( 2 ) 3 8 3 + . 2 - - +
- June 2018, AS Paper 1, Q6 (5 marks): In this question you must show detailed reasoning. ^ h 3 You are given that f x 4 x 3 x 1 . = - + ^ h is a factor of f x^ h. (i) Use the factor theorem to show
Questions, mark schemes and examiner’s reports are © OCR, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? OCR MEI A-Level Maths past papers.
The Plumi iPad app also offers exam-style questions with AI feedback on your handwritten working.