# 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. |

## Contents

## Arranging terms[edit]

Arrange the quadratic into order: first the squared number *ax ^{2}*, then the number times x,

*bx*, finally the constant value

*c*.

## Factorising quadratics[edit]

Form of quadratics:

To factorise:

- split the middle term so it adds to the original number, e.g., let b = (AD + BC), and
- multiplies to the constant times the first term, e.g., Ax times Bx equals ABx
^{2}, then a = AB, - 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: