Common Factoring | cutecute

Common Factoring and Grouping.

Common factoring is one of the way of factoring .

The FACTOR OF AN INTEGER is only number that divides evenly into the given integer.
For example; factors of 12 1,2,3, 4, 6,12.
The GREATEST COMMON FACTOR( GCF) is the largest integer that integer that divides evenly into each of a given set of numbers. For example; if we examine the factor of 4 and 8:

4: 1,2,4. 8 : 1,2,4,8.

GCF : 4

When factoring polynomial expressions, we need to examine both the numerical coefficients and the variables to find the GCF. We look for the greatest common numerical factor, and the variable common to each term. We are looking for a whole number factor.
To check that you have factored correctly, you can always expand your answer to make sure that you get what you started with because FACTORING IS THE OPPOSITE OF EXPANDING.
You can always check your factored answer by expanding.

Example 1) 14m + 21n

So when find the common factor, which in this case is 7.

7 (2m + 3n )

Another example is 3x^3 - 5x^2

There is no common factor between 3 and 5 however a common factor is x and you choose the variable with the lowest exponent. So here the common factor is x^2. So then, you would factor out the x^2

= x^2 (3x- 5)

An example of a word problem where you would use common factoring to factor the question.

Binomial Common Factoring.

Factor : 2x (x+5) + 3 (x+5)

In this case , we need to think of (x+5) as one factor. Therefore, you would write ( x + 5) outside the bracket, and write what’s left on the inside.

Solution: (x +5) (2x + 3)

Therefore, a binomial can also be considered a common factor.