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anonymous

  • one year ago

What is the factorization of the polynomial graphed below? Assume it has no constant factor.

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  1. anonymous
    • one year ago
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  2. zepdrix
    • one year ago
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    This polynomial has three distinct roots, and the shape of an odd function. So we should expect a third degree polynomial. One of the roots of this polynomial is \(\large\rm x=1\). See how it passes through x=1? :) Subtract 1 from each side,\[\large\rm x-1=0\]That tells us that one of the factors of our polynomial will be: \(\large\rm (x-1)\)

  3. zepdrix
    • one year ago
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    How bout the other roots? See any others? :)

  4. anonymous
    • one year ago
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    5 or 3 ?

  5. zepdrix
    • one year ago
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    Mmm 3 sounds good: \(\large\rm x=3\qquad\to\qquad (x-3)=0\) 5 also: \(\large\rm x=5\qquad\to\qquad (x-5)=0\)

  6. zepdrix
    • one year ago
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    So bam! There's your polynomial! :) Just multiply those factors together. \(\large\rm =(x-1)(x-3)(x-5)\)

  7. anonymous
    • one year ago
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    Thank you !

  8. zepdrix
    • one year ago
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    yay team \c:/

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