In this short post I wish to explain how to solve simple quadratic equations with Trinomial factorisation

To solve a quadratic equation in this form there are two main methods you can use to solve these either trinomial (also known as quadratic) factorisation or the quadratic formula. In this article I will explain the factorisation method.

In maths it is always easier to use an example than to explain with words alone.

Ex1: Solve by factorisation x² + 8x + 12 = 0

1.    Break into two brackets with an x in each:

> (x ) (x     )

2.    Find two numbers that add to give 8 and multiply to give 12. Then place in the other side of each bracket.   

> (x    6) (x    2)

3.    Put in the sign (+ of -) since the numbers are +ve use a plus sign.

> (x   +    6) (x   + 2)

4.    Multiply out to check:

  > (x   +    6) (x   + 2)

= x² x 8x + 12

5.    Re write as:

> (x   +    6) =0

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> (x   + 2) = 0

This gets more complicated when you use either –ve numbers or start with more than one x². Here is a worked example:

Ex2: Solve by factorisation 3x² + x – 4

>(3x   ) (x   )

> (2x 4) (x 1)

> (2x   +    4) (x    -   1)

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