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

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Presentation transcript:

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 1 Find 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 2  Find 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 prime 51 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 2x 2 + 6x, determine the GCF.

Now lets apply GCF to polynomials:  Given the polynomial Find the GCF of 40a 2 b and 48ab 4, determine the GCF.

Determine the GCF for each of the following:

Now let’s factor  Factor 7x+14 using the GCF Example 4

 Factor 9x - 33 using the GCF

 Factor x 2 + 8x using the GCF

Example 5 Factor using GCF

Factor these on your own looking for a GCF