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Factoring out the GCF

Factoring out the GCF. Objectives. To review what GCF means To practice finding the GCF of numbers, and terms with exponents To learn what factoring means To learn how to factor out the GCF from a polynomial. What is GCF?. GCF is short for Greatest Common Factor

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Factoring out the GCF

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  1. Factoring out the GCF

  2. Objectives • To review what GCF means • To practice finding the GCF of numbers, and terms with exponents • To learn what factoring means • To learn how to factor out the GCF from a polynomial

  3. What is GCF? • GCF is short for Greatest Common Factor • The greatest common factor is the biggest number that can be divided into both terms without a remainder • Example: What is the GCF of 64 and 28? What are all the numbers that will divide evenly into 64? 1, 2, 4, 8, 16, 32, 64 What are all the numbers that will divide evenly into 28? 1, 2, 4, 7, 14, 28 The Greatest Common Factor of 64 and 28 is 4

  4. GCF Practice • What is the GCF of 72 and 81? What are all the numbers that will divide evenly into 72? 24, 36, 1, 2, 3, 4, 6, 8, 9, 12, 18, 72 What are all the numbers that will divide evenly into 81? 1, 3, 9, 27, 81 The Greatest Common Factor of 72 and 81 is 9

  5. GCF Practice • What is the GCF of 24, 46, and 92? What are all the numbers that will divide evenly into 24? 1, 2, 3, 4, 6, 8, 12, 24 What are all the numbers that will divide evenly into 46? 1, 2, 23, 46 What are all the numbers that will divide evenly into 92? 1, 2, 4, 23, 46, 92 The GCF of 24, 46 and 92 is 2

  6. GCF Practice • Try these on your own • Find the GCF of each set of numbers • 1. 90, 76 • 2. 16, 40, 96 Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 Factors of 76: 1, 2, 4, 19, 38, 76 GCF = 2 Factors of 16: 1, 2, 4, 8, 16 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 GCF = 8 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

  7. GCF with variables • Sometimes we want to find the GCF of terms with variables. • First, find the GCF of the coefficients • Then find the GCF of the variables by looking for variables in common and using the one with the smallest exponent for each variable Example: Find the GCF of 28x3y7 and 21x2y9z 7 What is the GCF of the coefficients 28 and 21? x and y What variables do both terms have in common? What are the smallest exponents for x and y? x2 and y7 7x2y7 The GCF is:

  8. GCF Practice • What is the GCF of the following 3 terms? 18a3b9c 24ab4c3 30b5c8 What is the GCF of the coefficients 18, 24 and 30? 6 b and c What variables do they all have in common? b4 and c1 What are the smallest exponents for b and c? 6b4c The GCF is:

  9. GCF Practice • What is the GCF of the following 3 terms? 7de4f 25d2e4f9 35d3e5f2 What is the GCF of the coefficients 7, 25 and 35? 1 d, e and f What variables do they all have in common? What are the smallest exponents for d, e and f? d1, e4 and f1 1de4f or de4f The GCF is:

  10. GCF Practice • Try these on your own. • Find the GCF for each set of terms • 1. 15x4 30x2 • 2. 30m4k8r4 60m2k2 70mk5r2 15x2 10mk2

  11. What is factoring? • Factoring is like un-multiplying • To find the factors of a number we find what numbers could have been multiplied to get that number • We learned that with the distributive property • To factor 12x – 42 would mean to un-multiply it or break it back into 6(2x – 7) 6 (2x – 7 ) = 12x – 42

  12. Factoring Example • Factor the following as much as possible. 15x + 20 • The first thing we want to do is find the GCF of all the terms • Then divide each term by the GCF What is the GCF of 15x and 20? 5 These are the factors You can always multiply it out to double check your answer The factored form is 5(3x + 4)

  13. Factoring Practice • Factor the following: 30x3 + 14x5 What is the GCF of 30x3 and 14x5? 2x3 Divide each term by the GCF? These are the factors The factored form is 2x3(15 + 7x2)

  14. Factoring Practice • Factor the following: 12a2b3 + 9ab5 – 3a5b2 What is the GCF of all 3 terms? 3ab2 Divide each term by the GCF? These are the factors The factored form is 3ab2(4ab+3b3 – a4)

  15. Factoring Practice • Factor each of the following on your own • -30x – 45 • 27a2b3c4 + 54a5c6 + 18a4b2c -15(2x + 3) 9a2c(3b3c3 + 6a3c5 + 2a2b2)

  16. Factoring Practice • Factor each of the following on your own • 18p4r – 6p3 • 7a2b3c + 9b2d2 + 5b4d7 6p3(3pr – 1) b2(7a2bc + 9d2 + 5b2d7)

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