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Factorising

Factorising
  • You can write expressions as a product of their factors
  • Factorising is the opposite of expanding brackets

Quadratics

Factorising a Quadratic
  • Find two factors of \(ac\) that add up to \(b\)
  • Rewrite the b term as a sum of these two factors
  • Factorise each pair of terms
  • Take out the common factor
Example
  • \(2x^2+5x-3\)
  • \(2\) x \(-3 = -6\)
  • 6 and -1 are factors of ac and add to b
  • We can rewrite this as \((2x-1)(x+3)\) because 2x times by 3 makes 6x
\(25x-9x^3\)
  • Take out x as a factor: \(x(25-9x^2)\)
  • Factorise the quadratic using DOTS: \(x(5+3x)(5-3x)\)
  • Fully factorised.
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