Factoring - Extracting a Common Factor
For example, the expression 4(x+3) may be expanded into 4∙x+4∙3, which is 4x+12. Extracting a common factor out of 4x+12 means doing the exact opposite: reversing the expansion and turning 4x+12 into 4(x+3).
Once you get the idea, you don't really need to write down the factored form of every term (4∙x and 4∙3). If you feel comfortable with it, feel free to skip that step. It's sufficient to simply place the common factor in front of a pair of brackets, and populate the brackets by asking yourself "by what must I multiply 4 in order to receive each one of the terms?"
Go for it:
4x+24 = ?
Incorrect.
Remeber, you can check your work by expanding the brackets; the result should be the original expression.
6(x+4) =
---> 6∙x+6∙4
---> 6x+24
6x+24 isn't equal to our original expression 4x+24, meaning this answer is incorrect.
Give it another try:
Incorrect.
Remember, you can check your work by expanding the brackets; the result should be the original expression.
2(x+8) =
---> 2∙x+2∙8
---> 2x+16
2x+16 isn't equal to our original expression 4x+24, meaning this answer is incorrect.
Give it another try:
Try the next one yourself:
Alright. Get the following example right and win a ticket to the fast lane:
14xy-35x = ?
Good job.
Alright, we're convinced. Skip to the summary?
Let's sum it up:
[[summary]]
[[summary]]
Sure.
Extracting a common factor, also known as 'simple factoring', is the process of dividing factors evenly out of a group of numbers or variables, and placing them in front of a pair of brackets. In other words, it's the exact opposite of multiplying a single term with an expression in brackets.
To extract a common factor, your first step is to find the greatest common factor of the terms in question. In our example of 4x+12, both 4x and 12 contain a '4' factor, but no more - that's the greatest common factor.
To extract the '4' out of both terms, first break up each one of them into a multiplication of "4∙(something)". 4x is 4∙x, whereas 12 is 4∙3, so our expression equals:
4∙x+4∙3
Next, write down the '4' in front of a pair of brackets. Place the remaining factors of each of the terms inside the brackets, while keeping the "+" sign from the original expression:
4(x+3)
That's it! Once you're done, you can always check your work by expanding the brackets. If everything is in order, the result will be equal to the original expression: expanding 4(x+3) indeed results in our original 4x+12.
Correct.
The common factor of 4x and 24 is 4. Write 4 to the left of a pair of brackets, and populate the brackets with the remaining factors.
4x+24 =
---> 4∙(x+6)
Sure:
6x+15= ?
First, find the greatest common factor that can be extracted out of both terms. Effectively, this means finding the greatest numbers both terms are divisible by. In this case, both 6x and 15 are divisible by 3, but nothing greater than 3.
Next, rewrite 6x and 15 as multiplications of 3:
3∙2x+3∙5
Finally, extract the common factor to the left of a pair of brackets:
---> 3(2x+5)
Again, check your work by expanding the brackets back into the original 6x+15.
Incorrect.
No fast lane for you!
Incorrect.
No fast lane for you!
