Factorising
Watch this video to learn about factorising an expression
We factoriseTo put an expression into brackets. For example, 18x + 12y = 6(3x + 2y). Factorising is the reverse process to expanding. an expression by rewriting it as a product of factorA factor is a number which divides exactly into another number. 1 is a factor of every number and every number is a factor of itself. A number can have several factors. Example: 1, 2, 5 and 10 are the factors of 10.. If we think back to removing brackets, the answer is now the question and the question is now the answer. We should ask ourselves; 'What was it before we removed the brackets?'
A great trick when factorising is to multiply out the brackets once you've got an answer and you should find that your answer matches with the question. If it doesn't, then you know you've done something wrong.
Try the example questions below.
Question
Factorise \(10 + 4x\)
The first thing we do is find the highest common factor (HCF)The highest common factor (HCF) of two numbers is the largest number which will divide exactly into both of them, for example, the highest common factor of 24 and 36 is 12. (H.C.F) of \(10+4x\) and this will tell us the term that will go outside the bracket.
Factors of 10
Common factors are: -2, -1, 1 and 2.
Highest Common Factor (H.C.F.) of 10 and \(4x\) is 2.
\(10 + 4x = 2(... + ...)\)
To get the terms inside the bracket, we find \(2 \times ? = 10\) and then \( 2 \times ? = 4x\), namely 5 and \(2x\) respectively.
\(= 2(5 + 2x)\)
Remember you can multiply out your brackets now to check that your answer is correct.
Question
Factorise \(6a - 9\)
Highest Common Factor (H.C.F.) = 3.
\(6a - 9 = 3(2a - 3)\)
Question
Factorise \(15 + 10x\)
\(= 5(3 + 2x)\)
Question
Factorise \(3 - 12a\)
\(= 3(1 - 4a)\)
Question
Factorise \(20y - 6\)
\(= 2(10y - 3)\)
