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anonymous

  • 4 years ago

Solve: x^3-2x^2-5x+6=0

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  1. anonymous
    • 4 years ago
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    Please help!

  2. TuringTest
    • 4 years ago
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    first thing I do in these situations is check if you get lucky and have +/-1 be a solution...

  3. anonymous
    • 4 years ago
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    Answer: x= -2 , x= 1 and x = 3

  4. Mertsj
    • 4 years ago
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    Did you try synthetic division?

  5. anonymous
    • 4 years ago
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    No, I haven't tried synthetic division because I was unsure how to start it? Do I just pick number I think will work?

  6. Mertsj
    • 4 years ago
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    The factors of the constant term, which is 6, are +-1, +-2, +-3, +-6. Would you agree?

  7. Mertsj
    • 4 years ago
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    The coefficient of the x^3 term is 1. So the possible rational roots are the factors of the constant term divided by the factors of 1.

  8. anonymous
    • 4 years ago
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    Yes that makes sense. Okay, so now I try all of those numbers?

  9. Mertsj
    • 4 years ago
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    \[\pm1, \pm2,\pm3, \pm 6\]

  10. Mertsj
    • 4 years ago
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    i usually start with the small ones.

  11. Mertsj
    • 4 years ago
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    |dw:1327802691317:dw|

  12. Mertsj
    • 4 years ago
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    Look at that. We stumbled onto one first thing. That means that one factor is (x-1) And the other factor is x^2-x-6 which can then be factored by the usual methods.

  13. Mertsj
    • 4 years ago
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    So we have: (x-1)(x^2-x-6)= (x-1)(x-3)(x+2)=0 So x=1, 3, or -2

  14. anonymous
    • 4 years ago
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    I'm sorry, but could you explain how we got x^2-x-6? I understand how we found the first one but now I am rather lost

  15. Mertsj
    • 4 years ago
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    I will repost the synthetic drawing and then you will see.

  16. Mertsj
    • 4 years ago
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    |dw:1327802958637:dw|

  17. Mertsj
    • 4 years ago
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    It's the same as when you divide anything. Like 12 divided by 4 = 3 because 3 times 4 = 12

  18. anonymous
    • 4 years ago
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    Okay thank you. I understand now. You are a life saver!

  19. Mertsj
    • 4 years ago
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    S= x^3-2x^2-5x+6 divided by x-1 = x^2-x-6 because (x-1)(x^2-x-6)=x^3-2x^2-5x+6

  20. Mertsj
    • 4 years ago
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    You are very welcome.

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