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==Type 2==
 
==Type 2==
   
(Where the coefficient of x<sup>2</sup> is not a common factor)
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(Where the coefficient of x<sup>2</sup> is a common factor)
   
 
'''Method'''
 
'''Method'''

Latest revision as of 05:44, July 7, 2013

A quadratic expression is an expression with a highest power of x, as 2 or an equation with degree 2 and the general form is:


ax2 + bx+c where a, b and c are numbers.

Type 1Edit

(For an expression with a coefficient of x equal to 1, (a=1), the given method can be used to factorise)

Method

  1. Find 2 factors of the Constant Term (c), which should add to a coefficient of x
  2. Write the xpression as a product of two brackets, with a factor in each bracket

Examples

  1. Factorize x2 + 5x + 6
    • Factors of 6 that add to 5:
      • ​2 * 3 = 6
      • 2 + 3 = 5
    • Answer: (x + 2)(x + 3) OR (x + 3)(x + 2)
  2. Factorize x2 - 12x + 36
    • Factors of 36 that add to -12:
      • ​-6 * -6 = 36
      • -6 + -6 = -12
    • Answer: (x - 6)(x - 6) OR (x - 6)2
  3. Factorize x2 + 8x - 20
    • Factors of -20 that add to 8:
      • 10 * -2 = -20
      • 10 + -2 = 10 - 2 = 8
    • Answer: (x + 10)(x - 2) OR (x - 2)(x + 10)

Type 2Edit

(Where the coefficient of x2 is a common factor)

Method

  1. Factorise by having the common factor outside the bracket and a quadratic expression inside the bracket
  2. Furthur factorise the quadratic.

Type 3Edit

(Where the coefficient of x2 is not 1 (But not a common factor))

Method

  1. Write ax2 as two factors and c as two factors.
  2. Multiply the factors of ax2 with the factors of the constant term and they should add to bx
  3. Re-arrange the factors diagonally and write them in two brackets
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