Factorising quadratics

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Quadratic equations are equations of the form where a, b and c are constants, and is a variable. In other words, a quadratic equation has at least one term of the variable, say , raised to the exponent , e.g.

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Arranging termsEdit

Arrange the quadratic into order: first the squared number ax2, then the number times x, bx, finally the constant value c.

Factorising quadraticsEdit

Form of quadratics:  

To factorise:

  1. split the middle term so it adds to the original number, e.g., let b = (AD + BC), and
  2. multiplies to the constant times the first term, e.g., Ax times Bx equals ABx2, then a = AB,
  3. then bracket so the pronumeral (letter) is like this, e.g., (Ax + C)(Bx + D).

CheckingEdit

Multiplying the two terms:   and   with each other becomes:

 

which rearranges to:

 

The final constant  

ExamplesEdit

 

 

To check it, re-expand the answer to see if we get back to where we started from:

 

 

 

See alsoEdit

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Further readingEdit

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{{Mathematics resources}}