Factoring Quadratic Expressions of two terms by taking a common factor

The Method:

When a quadratic expression contains two terms, it can be factored by taking a common factor. A common factor is a number, variable, or a term that is present in both the terms of the quadratic expression. The common factored is taken outside of parenthesis, and the quadratic expression is written inside the parenthesis.


Example 1:  x2 + 3x

The common factor of the above quadratic expression is x because x is present in both the terms of the quadratic expression: In 'x2', there are two x's multiplying each other, and in '3x', there is an 'x'. Now when we can take 'x' as the common factor, 'x2' becomes 'x', and '3x' becomes '3'. This is because we have taken away one 'x' from each term. The resulting expression will be as follows:

x(x + 3)
Notice that taking out a common factor is the opposite process of FOIL method. So you can call it unFOILing as well.

Example 2:  4x2 + 4

The common factor in the above expression is 4, because 4 is present in both the terms. So you can factor out 4 as follows:

4(x2 + 1)
You might want to see the solved examples or the practice by a worksheet on factoring (by the method of taking a common factor).

1 comment:

  1. Here is the simple and clear definition of GCF that is When there are the factors of two or more numbers and some of the factors are the common, then the largest number from those common factors is called as the Greatest Common Factor.It is Abbreviated as GCF and Also known as Highest Common Factor.