Greatest+Common+Factor

The greatest common factor (GCF) is used when the quadratic expression allows you to divide out a value from each of the terms in the expression.

Finding the GCF of a set of numbers is easy. The first thing you should do is list all of the factors of the numbers you are trying to find the GCF of. Next, find all of the factors that are the same for each number. The greatest of these is your GCF.

Let's say you are trying to find the GCF of 24 and 32. First, list the factors. 24- 1, 2, 3, 4, 6, 8, 12, and 24 32, 1, 2, 4, 8, 16, and 32

Next, identify the factors that are the same. 24- __1__, __2__, 3, __4__, 6, __8__, 12, and 24 32- __1__, __2__, __4__, __8__, 16, and 32

Because 8 is the greatest factor that 24 and 32 have in common, it is the GCF.

Now that you have the GCF, you need to know how to divide it out of the quadratic expression.

If your expression is 8x 2 + 24x + 32, you will divide the 8, 24, and 32 values by their GCF of 8. 8/8 = 1 24/8 = 3 32/8 = 4 These numbers will replace the original values in the expression and the expression will be put into parenthesis and an 8 will be put on the outside of parenthesis. 8x 2 + 24x + 32 will become 8(x 2 + 3x + 4).


 * NOTE:** __ALWAYS__ try to factor out the GCF first. If it isn't possible, you will have to try a different method of factoring.

Ex: In the quadratic expression 3x 2 + 24x + 45, you can divide each term by 3.

When you do this, the value you divided by becomes the factor to the rest of the expression.

Ex: The expression 3x 2 + 24x + 45 would become 3(x 2 + 8x + 15).

Now that the expression is in the standard form of x 2 + bx + c, you need to reverse FOIL. If "x" has a coefficient that isn't 1, you should refer to the "Trinomials Where a Does Not = 1" page of this site.

Reverse FOILing is when you find the two values whose product is the "c" term in your quadratic expression and sum is the "b" term in your expression. These two numbers are separated into two binomials along with an "x".

For example: 3(x 2 + 8x + 15) will become 3(x + 3)(x + 5). This is your final answer. Note that if the "c" term is positive, the signs in both binomials will be the same and the sign of the "b" term is the sign you will put in both binomials. If the "c" term is negative, the signs will be different.

Take the quadratic expression 3x 2 - 12x - 63 for example.

First, you would factor the 3 out: 3(x 2 - 4x - 21)

Next, find the set of numbers whose product is -21 and whose sum is -4. In this case, 3 and -7.

Now separate them into two binomials, both containing an "x". 3(x + 3)(x - 7)

Written by Adam