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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


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August 9th, 2007, 05:07 AM   #1
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the hardest part in elementary school math is..

i've had a lot of hard time with fractions in arithmetic when i was young -- it was very hard! i'm serious! did this happen to any of you guys?
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August 9th, 2007, 01:37 PM   #2
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Nah, fractions were easy for me. The hardest part for me (harder than Algebra I and II!) was long division; I remember being in the last third of the class to pick it up.
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August 9th, 2007, 04:43 PM   #3
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Quote:
Nah, fractions were easy for me. The hardest part for me (harder than Algebra I and II!) was long division; I remember being in the last third of the class to pick it up.
Same here. I still can't remember how to do long polynomial division.
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August 9th, 2007, 06:21 PM   #4
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It's the same basic concept as long division in base 10 with the difference that you can have negative terms. For example:

(4x^4-3x^3+x^2-2x-5)/(x^2-1)

Code:
                 4x^2
      ____________________
x^2-1| 4x^4-3x^3+ x^2-2x-5
      -4x^4-0x^3+2x^2
      _______________
       0x^4-3x^3+3x^2



                 4x^2-3x
      ____________________
x^2-1| 4x^4-3x^3+ x^2-2x-5
      -4x^4-0x^3+2x^2
      _______________
       0x^4-3x^3+3x^2-2x
           +3x^3+0x^2-3x
           _____________
            0x^3+3x^2-5x



                 4x^2-3x+3
      ____________________
x^2-1| 4x^4-3x^3+ x^2-2x-5
      -4x^4-0x^3+2x^2
      _______________
       0x^4-3x^3+3x^2-2x
           +3x^3+0x^2-3x
           _____________
            0x^3+3x^2-5x-5
                -3x^2+0x+3
                __________
                 0x^2-5x-2
The quotient, then, is 4x²-3x+3, and the remainder is -5x-2.

Okay, that doesn't explain it very well , but did anyone follow any of it?
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August 10th, 2007, 02:56 AM   #5
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Code:
                 4x^2
      ____________________
x^2-1| 4x^4-3x^3+ x^2-2x-5
      -4x^4-0x^3+2x^2 ← ← ← ← ← ←
      _______________
       0x^4-3x^3+3x^2
Should that term by the arrows be a +4x^2? Or am I still suffering from polynomial division delusions?
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August 10th, 2007, 08:18 AM   #6
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Well, it looks like you followed it better than I did ! Yes that was a mistake on my part. That's part of the risk of doing math late at night .
Corrected version:
Code:
                 4x^2-3x+5 
     _____________________ 
x^2-1) 4x^4-3x^3+ x^2-2x-5 
      -4x^4-0x^3+4x^2 
      _______________ 
       0x^4-3x^3+5x^2-2x 
           +3x^3+0x^2-3x 
           _____________ 
            0x^3+5x^2-5x-5 
                -5x^2+0x+5 
                __________ 
                 0x^2-5x+0
Quotient: 4x²-3x+5
Remainder: -5x

This can be re-written as
4x^4-3x³+x²-2x-5=(4x²-3x+5)(x²-1)-5x

Or you could divide that equation by the divisor, but that's uglier in my opinion.
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