What is factorising?

Factorising is the reverse of expanding brackets. When you factorise a quadratic expression like x² + 5x + 6, you rewrite it as a product of two brackets: (x + 2)(x + 3).

This is one of the most common topics on the Junior Cycle maths exam, and once you learn the method, it’s quite straightforward.

The method: find two numbers

For a quadratic in the form x² + bx + c, you need to find two numbers that:

  • Multiply to give c (the constant term)
  • Add to give b (the coefficient of x)

Example 1: x² + 5x + 6

We need two numbers that multiply to 6 and add to 5.

  • 2 × 3 = 6 ✓
  • 2 + 3 = 5 ✓

So: x² + 5x + 6 = (x + 2)(x + 3)

Example 2: x² − 7x + 12

We need two numbers that multiply to 12 and add to −7.

  • (−3) × (−4) = 12 ✓
  • (−3) + (−4) = −7 ✓

So: x² − 7x + 12 = (x − 3)(x − 4)

Watch out for negatives

When the constant term is negative, one of your numbers will be positive and the other negative.

Example 3: x² + 2x − 8

Multiply to −8, add to +2:

  • 4 × (−2) = −8 ✓
  • 4 + (−2) = 2 ✓

So: x² + 2x − 8 = (x + 4)(x − 2)

Practice questions

Try these yourself:

  1. x² + 6x + 8
  2. x² − 5x + 4
  3. x² + x − 12
  4. x² − 9 (hint: difference of two squares)

Tips for the exam

  • Always check your answer by expanding the brackets back out
  • If you can’t find the two numbers quickly, write out all the factor pairs of c
  • Remember: difference of two squares is a special case — x² − 9 = (x + 3)(x − 3)

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