A simple method to factorise an expression into a double bracket. Expressions of the form x² + bx + c
Expressions of the form x² + bx + c can be factorised into a double bracket. Basically you are looking for two numbers that multiply to give c and add to give b.
Question 1 on double bracket factorisation
Factorise:
x² -5x + 6
To begin with write down all the factor pairs of +6 (the number at the end). These are:
1 × 6
2 × 3
-1 × -6
-2 × -3
Notice that all the pairs have the same signs when the number at the end is positive.
Now one of these factor pairs must add to give you -5 (the number before x)
1 + 6 = 7
2+ 3 = 5
-1 + -6 = -7
-2 + -3 = -5
So the last pair gives -5.
Therefore the expression can be written down as (x-2)(x-3) or (x-3)(x-2) as it doesn’t matter which bracket you write down first.
Question 2 on double bracket factorisation
Factorise:
x² + 6x -7
To start off with write down all the factor pairs of -7 (the number at the end). These are:
1 × -7
-1 × 7
Notice that the pairs have different signs when the number at the end is negative.
Now one of these factor pairs must add to give you 6 (the number before x)
1 + -7 = -6
-1 + 7 = 6
So the last pair gives +6.
Therefore the expression can be written down as (x-1)(x+7).
Question 3 on double bracket factorisation
Factorise:
x² -9x -10
To start off with write down all the factor pairs of -10 (the number at the end). These are:
1 × -10
-1 × 10
2 × -5
-2 × 5
Again since the number at the end is negative all the pairs have different signs.
Yet again, select the pair of factors that gives you the number before x which is -9.
1 + -10 = -9
-1 +10 = 9
2 + -5 = -3
-2 + 5 = 3
So the first pair gives you -9.
Therefore the expression can be written down as (x+1)(x-10).
If you are finding these examples difficult then take a look at this other article on double bracket factorisation.
For harder examples on double bracket factorising then click here.