Factorising quadratics

Educational level: this is a secondary education resource.

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.

Subject classification: this is a mathematics resource.

Arranging terms Edit

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

Factorising quadratics Edit

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).

Checking Edit

Multiplying the two terms:   and   with each other becomes:


which rearranges to:


The final constant  

Examples Edit



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




See also Edit

References Edit

Further reading Edit

External links Edit

{{Mathematics resources}}