Algebra 7 Point 1

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Algebra 7 Point 1

  1. 1. 7.1 Introduction to Factoring<br />Objectives: <br /><ul><li>To find the GCF of 2 or more integers
  2. 2. To find the GCF of two or more monomials
  3. 3. To find the missing factor, given a monomial and one of its factors.</li></ul>Frameworks: 10.P.5<br />
  4. 4. How could you rearrange 12 tiles to form a rectangle?<br />
  5. 5. Factoring<br />To factor an integer means to express it as the product of 2 or more integers.<br />12 = 1 x 12<br />12 = 2 x 6<br />12 = 3 x 4<br />
  6. 6. Factoring<br />12 = 2 x 6 could also be expressed as<br />12 = 2 x 3 x 2<br />In the second case, none of the factors can be factored further without using the factor 1. <br />2 and 3 are called prime numbers<br />
  7. 7. Prime Numbers<br />A prime number is an integer greater than 1 whose only positive factors are 1 and itself.<br />Can you think of examples?<br />1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31<br />
  8. 8. Composite Numbers<br />A composite number is a positive integer that has two or more positive factors other than 1<br />Can you think of examples?<br />4, 6, 8, 9, 10, 12, 14, 15<br />1 is neither prime nor composite<br />
  9. 9. Prime factorization<br />A factorization where all the factors are prime numbers<br />12 = 2 x 2 x 3<br />36 = 2 x 2 x 3 x 3<br />
  10. 10. Give the prime factorization of 90:<br />Choose 2 positive factors of 90. Continue factoring until all the factors are prime numbers.<br />
  11. 11. Give the prime factorization of 100:<br />Choose 2 positive factors of 100. Continue factoring until all the factors are prime numbers.<br />
  12. 12. Can there be more than 1<br />prime factorization of a number?<br />No.<br />
  13. 13. GCF – Greatest Common Factor<br />The greatestcommon factor (GCF) of two or more integers is the largest integer that is a factor of all the integers.<br />
  14. 14. Find the GCF of 72 and 84<br />72 = 12 * 6 =<br />84 = 14 * 6 =<br />
  15. 15. Find the GCF of 36 and 90<br />
  16. 16. Find the GCF of 12x4 and -28x3 and 120 x2<br />
  17. 17. Find the GCF of 84y3and -96y6and -196y5<br />
  18. 18. To find a missing factor, divide.<br />For example, <br /> x3 * ____ = x7<br /> x7 <br /> x3<br />So, the answer is x4<br />
  19. 19. Find the missing factor:<br />a5 * ____ = a9<br />___ * 5a = -30a10<br />3a3b5 * ____ = 24a4b7<br />
  20. 20. Do p. 246 1-21<br />
  21. 21.
  22. 22. FOIL Review<br />(x + 3)(x + 5)<br />First terms: x and x x2<br />Outside terms: x and 5 5x<br />Inside terms: 3 and x 3x<br />Last terms: 3 and 5 15<br />Answer: x2 + 8x + 15<br />
  23. 23. FOIL pattern . . .<br />
  24. 24. Homework<br />

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