How To Factorise Quadratics!

Step by Step Guide to Factorising Quadratic Expressions

All quadratic equations look like this (which we call the general equation):

ax² + bx + c = 0

It s important to note that all quadratics equal zero (like shown above) and the x s in the equation above could be another letter in different questions but this doesn t really mean anything different, you still follow the steps in this guide but instead of writing x, you write y (or any other letter that is given in the question).

Worked Example:

We have the following quadratic equation and we want to factorise it:

x² + 5x + 6

Step 1:

List the a, b and c values for this particular expression:

a = 1

b = 5

c = 6

Step 2:

List your ac (i.e. a value multiplied by the c value) and your b value:

ac = a x c = 1 x 6 = 6

b = 5

Step 3:

Now we want to find two numbers that multiply to give your ac value (i.e. 6 in this case)

AND also add to give your b value (5 in this case).

ac = 6 = 6 x 1

b = 5 = 6 + 1

Step 4:

Now sub the two numbers found in step 3 back into your quadratic expression in place of the b value:

x² + 6x + x + 6

Step 5:

Split the expression found in step 4 down the middle.

x² + 6x + x + 6

So now you have:

x² + 6x and x + 6

Step 6:

Factorise both sides of the split equation from step 5.

x² + 6x x + 6

x (x + 6) 1 (x + 6)

It is important tip to remember that after factorising the brackets highlighted in dark blue above should be the same. It s a nice quick check you can do to make sure you are going along the right path.

Step 7:

Now take the terms (in italics below) and put them into a bracket of their own (remember your signs!). Then take the other bracket and put it beside the bracket you created.

x (x + 6) 1 (x + 6)

Once you do this you have your final answer:

(x + 1) (x + 6)