Sunday, December 17

# Double Bracket Factorising. An Easy Method to Factorise a Double Bracket Expression.

If you are asked to factorise an expression then you will need to rewrite the expression either as a single bracket or a double bracket. An expression in the form x² + bx + c can be rewritten as a double bracket. Note that b and c are whole numbers (either negative or positive)

Step 1   Write down your double brackets.

(x + ?)(x+ ?)

Step 2   Write down all the factors pairs of c. That is all the pairs of numbers that multiply to give c.

Step 3   Out of the pairs of factors that you have just written down decide which pair of factors add (or take) to give you b.

Step 4   Fill this pair of factors back into the brackets in step 1.

Basically, you are looking for a pair of numbers that multiply to give you the last number (c) and add to give you the number before x (b).

The example on factorisation shown below is of an expression which can be factorised into a double bracket and the number before x² is always equal to 1 (since 1x²=x²)

Example 1

Factorise x² + 6x + 8

First of all notice that the form of the expression is a double bracket expression.

Step 1   Write down your double brackets.

(x + ?)(x+ ?)

Step 2   Write down all the factors pairs of c. That is all the pairs of numbers that multiply to give c.

These are:

1 × 8

2 × 4

Also remember that two negatives multiply together to give you a positive number, so you can also write down:

-1 × -8

-2 × -4

Step 3   Out of the pairs of factors that you have just written down decide which pair of factors add (or take) to give you b.

So we are looking for the pair of factors that gives +6 if you ignore the multiplication signs:

1 + 8 = 9

2 + 4 = 6

-1 – 8 = -9

-2 – 4 = -6

So the pair of factors that you use is 2 and 4

Step 4   Fill this pair of factors back into the brackets in step 1.

(x + 2)(x+4)