3 easy steps to make factorisation easy!

Look for a common factor. This means that you need to find a number or letter (or both) that you can divide every term by.

e.g.

3a^2 + 9a + 15a^4

= 3a ( a + 3 + 5a^3 )

AFTER taking out a common factor, look for one of the two special cases:

• Difference Of Two Squares (DOTS)
  • look out for two terms, both square numbers, with a minus sign between them
  • 25a^2 - 4
  • (5a - 2) (5a + 2)
• Pairing
  • 4 terms, each one containing a different pair of letters/numbers
  • factorise them in pairs
  • su + sv + tu +tv
  • s ( u + v ) + t ( u + v )
  • ( s + t ) ( u + v )

FINALLY, look for trinomials.

• three terms
• can only be factorised if in the following form:
• ax^2 + bx + c
• (a, b and c are numbers)

-- x^2 + 5x + 4

-- ( x + 4) ( x + 1 )

1) 3x + 12

2) x^2 - 16

3) pq + pr + sq + sr

4) x^2 + 4x - 12

5) 2pq + 2pr + 2sq + 2sr

1) 3 ( x + 4 )

2) ( x + 4 ) ( x - 4 )

3) ( p + s ) ( q + r )

4) ( x + 6 ) ( x - 4 )

5) 2 { ( p + s ) ( q + r ) }