Whenever you need to factor an algebraic expression, the very first thing you should always check is: Do these algebraic expressions have a common factor?

In other words, is the GCF of these two expressions something other than 1? Then we can use that GCF to factor the expression.

Example 1: Factor the expression 12x² + 4x.

Solution: First we find the GCF of these two expressions: 4x.

Now we need to take both terms in our algebraic expression and divide them by 4x.

What do you get when you divide 12x² by 4x? You get 3x. What do you get when you divide 4x by 4x? You get 1.

The answer, then, is 4x(3x + 1).

If you're not sure about your answer, use the distributive property to make sure that 4x(3x + 1) is the same as 12x² + 4x!

Example 2: Factor the expression 8x³y - 6x.

Solution: The GCF of the two terms is 2x.

Dividing 8x³y by 2x gives 4x²y, and dividing 6x by 2x gives 3.

The factored expression, then, is 2x(4x²y-3)

Example 3: You can also use this process when you have more than two terms: Factor x³ - 4x² + 2x.

The GCF of these three terms is just x.

Dividing each of the three terms by x gives x², - 4x, and 2.

So the answer is:

x(x² -4x + 2)