What is common factoring and how to common factor?

 

Common factoring is figuring out the number that is a factor of all the terms in an expression. 

Then, taking out that number, and multiplying it by another number, so that their product is the original expression.

 

For example, 3x+6

• In this expression let's first find out the factors of both numbers.

• Factors of 3 are 1 and 3.

• Factors of 6 are 1,2,3, and 6.

What is the common factor?

• In this case, it is 3 because 3 is a factor of both 3 and 6.

• Now take out the common factor, so it becomes 3(____).

• Find out which number and variable multiply with 3, in order to make 3x.

• In this case 3 multiplied by 1x is equal to 3x, since 3x1=3, and 3 multiplied by x=3x.

• So it will become 3(x___).

Remember that if the co-efficient in front of the variable is 1, you do not need to write the 1.

• Now let's find out which number multiplies by 3, in order to make 6.

• So 3x__=6

• In this case, 3x2=6.

• Therefore, it will be 3(x+2).

 

The answer for this example is 3(x+2).

 

To check if the answer is correct, expand it, and see if you get the expression we originally started with.

• 3(x+2)

• Since the 3 is outside the brackets, it means that it has to multiplied with everything that is inside the brackets.

• 3 mulitplies with x and the 2.

• 3 multiplied by x equals to 3x.

• 3 multiplied by 2 equals to 6.

• So we get 3x+2, and this was the original expression, proving that our answer is correct.

 

 

In order to find out what some of the terms that will be used are, visit this site-http://www.mathsisfun.com/algebra/definitions.html

 

 

Video time!!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Try these examples...

1) 6x+4

2) x^2+2x

3) 2x^2+2x

4) 16x^2y-12xy^3

 

 

 

Answers would be...

 

 

 

 

1) 2(3x+2)

2) x(x+2)

3) 2x(x+1)

4) 4xy(4x-3y^2)