Paper 1 · Algebra ⏱ Tested in 5 exam questions since 2023 Lesson 13 of 23

Algebra 13 – Long division

In this lesson you’ll learn to

  • Find an unknown coefficient k two ways: root substitution or long division
  • Carry letter coefficients through polynomial long division
  • Divide a cubic by a quadratic factor and set both remainders to zero
  • Insert a 0x² placeholder and substitute between remainders in prove questions

Most recent exam questions

  • 2025 Paper 1 Q1(c) — factor theorem + polynomial long division + quadratic factoring
  • 2025 Paper 1 Q3(c) — cubic with all real coefficients, given one complex root — use the conjugate-pair theore…
  • 2024 Paper 1 Q6(a) — factor theorem — (x − a) is a factor of p(x) ⟺ p(a) = 0
  • 2024 Paper 1 Q7(b)(ii) — factor a cubic given one known root — use polynomial long division by the linear factor…
  • 2023 Paper 1 Q1(c) — polynomial long division — quadratic divisor, letter coefficients in the dividend, missi…
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