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Algebraic expressions and factoring sheet
Structured-answer frame

Factorise fully: (a) 3x² − 12 (b) 6x² − x − 2. Show your checks.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Look for a common factor first. (a) 3x² − 12 = 3(x² − 4).
  2. 2 · Spot the difference of two squares. x² − 4 = (x + 2)(x − 2), so 3x² − 12 = 3(x + 2)(x − 2).
  3. 3 · For (b) find ac and the two numbers. ac = 6 × (−2) = −12. Numbers with product −12 and sum −1: −4 and 3.
  4. 4 · Split and group. 6x² − 4x + 3x − 2 = 2x(3x − 2) + 1(3x − 2) = (2x + 1)(3x − 2).
  5. 5 · Check by expanding. (2x + 1)(3x − 2) = 6x² − 4x + 3x − 2 = 6x² − x − 2. ✓