Paper 1 · Algebra ⏱ Tested in 5+ recent exam questions Lesson 11 of 23

Algebra 11 – Solving cubic equations

You’ll learn

  • Find a first root of a cubic by trial and error (x = 1, −1, 2, −2, …)
  • Convert the root to a factor and divide it out by polynomial long division
  • Factorise the remaining quadratic to read off all three roots
  • Handle non-monic cubics whose factors give fractional roots like x = ½

Formula used

Roots of the quadratic equation

x = (-b ± √(b² − 4ac)) / 2a

On page 20 of the log tables — read it off, don’t memorise.

Most recent exam questions

  • 2025 P1 Q1(c)
  • 2024 P1 Q7(b)(i) — deferred
  • 2024 P1 Q7(b)(ii) — deferred
  • 2023 P1 Q4(b)(i) — deferred
  • 2023 P1 Q4(b)(ii) — deferred
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