Factorising quadratics

Description

Reduce a quadratic expression into two brackets. This process is the reverse of Expanding quadratics

e.g. $x^2+3x+2=(x+1)(x+2)$

To do this, when looking at the general form of a quadratic equation $(ax^2+bx+c)$ we identify the pairs of factors of $c$ which add to give $b$. In the above case there is only one pair of factors of c (2) that is to say, +1 x +2. In order to make b (3) we must add both of these together.

Example 2: $x^2-x-6$

Here, the factors of c (-6) are several. We could have:

• +1 x -6
• -1 x +6
• +2 x -3
• +3 x -2

We now need to pick the pair of factors which will add together to give our b term which is -1 (as in $-1x$ which is shortened by convention to $-x$). This would be the third pair +2 x -3 which when we add together give -1 (+2 + (-3))

To finish, we put the factor pair into double brackets like so:

$x^2-x-6=(x+2)(x-3)$

I would always recommend, especially at first, to expand your answers again using the 'FOIL' method to see if you get your original expression. It only takes a couple of seconds and can really save you some marks!

Links

Basic factorising