Factoring using GCF Tuesday August 14th 2012

GCFGreatest CommonFactor

What is a factor?Lets look at the factors of 36:

1, 2, 3, 4, 6, 9, 12, 18, 36

What is a factor?

You list the factors of 12:

1, 2, 3, 4, 6, 12

What are the common factors of 12 and 36?

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

12: 1, 2, 3, 4, 6, 12

Of these factors, which is the greatest or the GCF?

Example 1Find the GCF of 30 and 42

common factor is a whole number that is a factor of each number.

greatest common factor (GCF) is the greatest of their common factors.

Caution:Do not confuse GCF with LCM.

Example 2Find the LCM of 10 and 15

A multiple of a whole number is the product of the number and any nonzero whole number. A common multiple of two or more whole numbers is a multiple of each number. The least common multiple (LCM) of two or more whole numbers is the least of their common multiples.

Now lets apply GCF to polynomials:

Given the polynomial 2x + 10, determine the GCF.

Example 3

Now lets apply GCF to polynomials:

Given the polynomial 6x-2y, determine the GCF.

Now lets apply GCF to polynomials:

Given the polynomial 2x2 + 6x, determine the GCF.

Now lets apply GCF to polynomials:

Given the polynomial Find the GCF of 40a2b and 48ab4, determine the GCF.

Determine the GCF for each of the following:1.

2.

3.

4.

5.

Now let’s factor

Factor 7x+14 using the GCF

Example 4

Factor 9x - 33 using the GCF

Factor x2 + 8x using the GCF

3 2 2: 6 12 3Example c d c d cd

Example 5

Factor using GCF

Factor these on your own looking for a GCF.

1. 6x3 3x2 12x

2. 5x2 10x 35

3. 16x3y4z 8x2y2z3 12xy3z 2

6.

7.

8.