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Thread: Help!

  1. #1
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    Help!

    I need help desperately!
    I am having problems with-what else? Divining polynomials.
    I tried to post this once and somehow all my writing did not get posted properly. Okay here is the original problem:
    a^8+a^6+a^4+3a-1 by a+1

    So I add the missing powers: 7, 5,3, 2
    Then I get for the begging of the quotient:
    a^7
    then:-a^6
    So I multiply (+) 1 by (-)a^6 and I get -1a^6 correct? Because multiplying in algebra is: opposite=negative and same=positive
    So, I try subtracting -1a^6 from +a^6, and they are saying it is wrong. Where did I slip? They are saying the next quotient is 2a^5? I was thinking in my head "what?"

    I hope I am not bugging you great guys,
    Amy
    trying hard

  2. #2
    Senior Member skeeter's Avatar
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    Code:
          a^7-a^6+2a^5
           ---------------------------------------------------------
    a+1 | a^8+0a^7+a^6+0a^5+a^4+0a^3+0a^2+3a-1
          a^8+ a^7
          --------------
              -a^7+a^6+0a^5+a^4+0a^3+0a^2+3a-1
              -a^7-a^6
              -----------------
                  2a^6+0a^5+a^4+0a^3+0a^2+3a-1
                  2a^6+2a^5
                 -------------------
                      -2a^5+a^4+0a^3+0a^2+3a-1
    can you finish?

  3. #3
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    Skeeter,
    do you mean that because they are both opposite we add?
    Then a+a= 2 and keep the same power?
    Okay.. I am trying.
    Yuck.. I feel sick. not because of you though
    trying hard

  4. #4
    Senior Member skeeter's Avatar
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    you do understand that you are subtracting the lower line of terms from the upper ... when you subtract a negative value, what happens?

  5. #5
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    Say you are subtracting -5x from +7x:
    +7x
    - 5x
    ===
    +12x

    I find the easiest way "to make sure" is check by going backward:
    12x - 5x = 7x
    I'm just an imagination of your figment !

  6. #6
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    I think I got it

    Okay, so we bring down the a^5
    and times the divisor 1 by +2a^5
    and we get +2a^5
    and we take away that from 0a^5
    and we get negative 2a^5?

    The answer is (I think)
    a^7-a^6-2a^4-2a^3-2a^2-2a+5
    remainder=-4

    hopefully I am right.
    Well got to go!
    Love,
    Amy
    trying hard

  7. #7
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    Re: Help!

    Quote Originally Posted by BabyBlue - Emphasis Added
    I am having problems with-what else? Divining polynomials.
    That is an absolutely hilarious typo! It does descibe how some students approach polynomials. I am glad to see that you are trying to be a bit more down-to-earth about it.

  8. #8
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    Re: I think I got it

    Quote Originally Posted by BabyBlue
    and times the divisor 1 by +2a^5
    No, you multiply it.
    and we take away that from 0a^5
    No, you subtract it.

    Were you not ever mercilessly forced to do long division in grammar school? Really, it is EXACTLY the same,

  9. #9
    Elite Member stapel's Avatar
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    Quote Originally Posted by tkhunny
    Were you not ever mercilessly forced to do long division in grammar school?
    Quite possibly not. Modern progressive (new-new) educationist thought says that there is no need for students to do long numerical division, since calculators can do it for them. Many curricula have had this topic specifically removed, and this is regarded by many educationist authorities, such as the NCTM, as being a good thing.

    Of course, then we tutors and college teachers have to teach this elementary-school topic to our students, in order to explain so many other topics, lo, these many years later. Oy.

    Eliz.

  10. #10
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    People,
    I am still here
    trying hard

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