plumiPolynomials and the factor theorem: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on B.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.
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All 11 questions on Polynomials and the factor theorem, as a list
- June 2024, Paper 1, Q1 (1 mark): Find the coefficient of x in the expansion of (4x3 – 5x2 + 3x – 2)(x5 + 4x + 1) Circle your answer. [1 mark] –5 –2 7 11
- June 2024, Paper 1, Q3 (1 mark): The expression 12x2 + 3x + 7 3x – 5 can be written as Ax + B + C 3x – 5 State the value of A Circle your answer. [1 mark] 3 4 7 9
- June 2024, Paper 1, Q13 (6 marks): (a) It is given that P(x) = 4x3 + 8x2 + 11x + 4 Use the factor theorem to show that (2x + 1) is a factor of P(x) [2 marks] 13 (b) Express P(x) in the form P(x)
- June 2023, Paper 3, Q6 (9 marks): (a) Sketch the curve with equation y = x2(2x + a) where a > 0 [3 marks] O y x 6 (b) The polynomial p(x) is given by p(x) = x2(2x + a) + 36 6 (b) (i) It is given
- June 2022, Paper 1, Q11 (10 marks): The polynomial p(x) is given by p(x) = x3 + (b + 2)x2 + 2(b + 2)x + 8 where b is a constant. 11 (a) Use the factor theorem to prove that (x + 2) is a factor of
- November 2021, Paper 1, Q13 (8 marks): (a) Given that P(x) = 125x3 + 150x2 + 55x + 6 use the factor theorem to prove that (5x + 1) is a factor of P(x). [2 marks] 13 (b) Factorise P(x) completely. [3
- November 2021, Paper 3, Q2 (1 mark): Simplify fully (x + 3)(6 − 2x) (x − 3)(3 + x) for x 6= ×3 Circle your answer. [1 mark] −2 2 (6 − 2x) (x − 3) (2x − 6) (x − 3)
- November 2021, Paper 3, Q6 (4 marks): Given that x > 0 and x 6= 25 , fully simplify 10 + 5x − 2x 1 2 − x 3 2 5 − x p Fully justify your answer. [4 marks]
- November 2020, Paper 3, Q4 (7 marks): p(x) = 4x3 − 15x2 − 48x − 36 4 (a) Use the factor theorem to prove that x − 6 is a factor of p(x). [2 marks] 4 (b) (i) Prove that the graph of y = p(x) intersec
- June 2019, Paper 2, Q4 (4 marks): x2 + bx + c and x2 + dx + e have a common factor (x + 2) Show that 2(d − b) = e − c Fully justify your answer. [4 marks]
- June 2018, Paper 1, Q12 (10 marks): p(x) = 30x3 − 7x2 − 7x + 2 12 (a) Prove that (2x + 1) is a factor of p(x) [2 marks] 12 (b) Factorise p(x) completely. [3 marks] 12 (c) Prove that there are no r
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