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Understanding Factoring Using Greatest Common Factor (GCF) | Tuesday, August 14th, 2012

Learn the concept of factors, common factors, and GCF through examples involving numbers and polynomials. Discover how to find the GCF and apply it to factor expressions. Be cautious not to confuse GCF with LCM. Practice factoring with GCF on your own.

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Understanding Factoring Using Greatest Common Factor (GCF) | Tuesday, August 14th, 2012

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  1. Factoring using GCFTuesday August 14th 2012

  2. GCF • Greatest • Common • Factor

  3. What is a factor? Lets look at the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

  4. What is a factor? You list the factors of 12: 1, 2, 3, 4, 6, 12

  5. 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?

  6. common factor is a whole number that is a factor of each number. greatest common factor (GCF) is the greatest of their common factors. Example 1 Find the GCF of 30 and 42

  7. Caution:Do not confuse GCF with LCM. 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. Example 2 • Find the LCM of 10 and 15

  8. Now lets apply GCF to polynomials: • Given the polynomial 2x + 10, determine the GCF. Example 3

  9. Now lets apply GCF to polynomials: • Given the polynomial 6x-2y, determine the GCF.

  10. Now lets apply GCF to polynomials: • Given the polynomial 2x2 + 6x, determine the GCF.

  11. Now lets apply GCF to polynomials: • Given the polynomial Find the GCF of 40a2b and 48ab4, determine the GCF.

  12. Determine the GCF for each of the following: 1. 2. 3. 4. 5.

  13. Now let’s factor • Factor 7x+14 using the GCF Example 4

  14. Factor 9x - 33 using the GCF

  15. Factor x2 + 8x using the GCF

  16. Example 5 Factor using GCF

  17. Factor these on your own looking for a GCF. 6. 7. 8.

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