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Page accessed [ ] times since 1 June 2006
Page written by Judy Edwards, Thomasin Smith and Kee Teo with assistance from Rebecca Keen.
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FactorizationPolynomialsYou are probably familiar with the process of "multiplying out", that is to say, using the distributive law to express a product as a sum of terms. For example: 3(x + 2) = 3(x) + 3(2) = 3x + 6. Sometimes, especially when solving equations, it is useful to reverse the process of "multiplying out", that is to say, to express the sum of a number of terms as a product. This process is called factorisation. There are a number of ways of doing this, but by far the most important in practice is what is called "taking out a common factor". Essentially, this is just applying the distributive law in reverse. For example, multiplying out gives 3(x + 2) = 3(x) + 3(2) = 3x + 6. Looking at it the other way round, suppose we start with the expression 3x + 6. Notice that since 6 = 3(2), we can write the expression as 3(x) + 3(2), where 3 is a factor of both terms (we call it a common factor of the terms). Now we can apply the distributive law in reverse: 3x + 6 = 3(x) +3(2) = 3(x + 2) and so we have factorised the expression by taking the common factor 3 and putting it outside the brackets. A factor does not have to be an explicit number, it may be a variable (letter x in this case).
Have a go at these now.
Now you can use your factor-spotting skills to factorise expressions. Here is one more example to remind you how it works:
Sometimes a common factor may itself be a sum of terms.
Here are a few like this for you to practice on:
Common factors may also involve functions such as trigonometric or exponential functions.
Factorisation Index | Trigonometric Functions >>
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Exercise
1
