3 easy steps to make factorisation easy!

Follow these three steps in the exam, and you cannot make a mistake in a factorising question (just make sure you follow them in the right order!).

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  • Created by: Tiula
  • Created on: 29-04-10 20:27

Common Factor

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 )

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Special Cases

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 )
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Trinomials

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 )

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Some examples to try:

1) 3x + 12

2) x^2 - 16

3) pq + pr + sq + sr

4) x^2 + 4x - 12

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

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Answers:

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 ) }

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Comments

becky

Is the answer to number two correct?

good explaination though :)

Tiula

Yeah it is, only the question should be x^2 - 16, not +

Thanks, I'll just edit that :)

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