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← Multiply Rational Expressions 3 Factor - Visualizing Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. These are the correct factors for each part of the fractions. I know factoring
  2. can be tough, so if you're getting at least half of these right, great work. If
  3. you got stuck on one of these, try to look back at your work and see where you
  4. went wrong to get these factors. If you can't find an error in your work then
  5. stay with me for this solution. For our first numerator we can pull out a 2x
  6. from each term. So we'll have 2x times x squared minus 6x plus 9. Then we notice
  7. that this is a special factoring pattern. It's a perfect square trinomial. So we
  8. have 2x times x minus 3, times x minus 3. This gives us our first numerator. For
  9. this denominator, we want to find the factors of negative 12, that sum to
  10. negative 4. This allows us to rewrite our middle term. And then we'll use
  11. factoring by grouping to get 3x plus 2 times x minus 2. This is our factored
  12. form for our first denominator. For this numerator we want to find the factors
  13. of 12 that sum to negative 8. These two factors are negative 6, 6 and negative
  14. 2. We'll use factoring by grouping to get 3x minus 2 time x minus 2 for this
  15. numerator. And finally for this last denominator we pull out a 6x from both
  16. terms leaving us with 6x times x squared minus 9. Then we can factor this
  17. difference of squares using x plus 3 times x minus 3. This difference of squares
  18. pattern appears in all sorts of math. So it's great that we can recognize it
  19. quickly.