FANDOM


(Adding categories)
(Added Examples to Type 1)
Line 1: Line 1:
 
 
A quadratic expression is an expression with a highest power of x, as 2 or an equation with degreee 2 and the general orm is:
 
A quadratic expression is an expression with a highest power of x, as 2 or an equation with degreee 2 and the general orm is:
   
Line 13: Line 12:
 
#Find 2 factors of the [[Constant Term]] (c), which should add to a coefficient of x
 
#Find 2 factors of the [[Constant Term]] (c), which should add to a coefficient of x
 
#Write the xpression as a product of two brackets, with a factor in each bracket
 
#Write the xpression as a product of two brackets, with a factor in each bracket
+
'''Examples'''
  +
#Factorize x<sup>2</sup> + 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)
  +
#Factorize x<sup>2</sup> - 12x + 36
  +
#*Factors of 36 that add to -12:
  +
#**​-6 * -6 = 36
  +
#**-6 + -6 = -12
  +
#*Answer: (x - 6)(x - 6) OR (x - 6)<sup>2</sup>
  +
#Factorize x<sup>2</sup> + 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 2==
 
==Type 2==
   

Revision as of 05:47, June 23, 2013

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


ax^2 + bx+C where a, b and c are numbers.

Type 1

(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 2

(Where the coefficient of x^2 is not 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 3

(Where the coefficient of x^2 is not 1 (But not a common factor))

Method

  1. Write ax^2 as two factors and c as two factors.
  2. Multiply the factors of ax^2 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
Community content is available under CC-BY-SA unless otherwise noted.