Factoring using GCF interpret parts of an expressions such as terms, factors, and coefficient

What is a factor?

Lets recall the factors of 36:

Why are these factors of 36?

What is a factor?

You list the factors of 12:

What are the common factors of 12 and 36?

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

Example 1Find the GCF of 30 and 42

For two or more nonzero whole numbers, a common factor is a whole number that is a factor of each number. The greatest common factor (GCF) of two or more nonzero whole numbers 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.

Also recall that, when factoring,...

A prime number is a number that can only be divided by only one and

itself.A composite number is a number greater than one that is not prime.

Prime or composite?37

prime51

composite

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.