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Poly Factoring

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data
    determine the interval algebraically for -2(x-1)(2x+5)(x-7)>0

    3. The attempt at a solution
    the zeroes are 1. -2.5, 7

    what do i do with the -2 in front?
  2. jcsd
  3. Mar 31, 2009 #2


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    Homework Helper

    If you graph [tex]y=(x-1)(2x+5)(x-7)[/tex] and then multiply the function by 2, so now you have the graph [tex]y=2(x-1)(2x+5)(x-7)[/tex] and finally, take the negative.

    Now do you know what [tex]y=-2(x-1)(2x+5)(x-7)[/tex] looks like?
  4. Mar 31, 2009 #3
    i think ive figured it out, so basically i would divide both sides by -2, and when i divide and an equality by a -, i will hav eot change the direction of the sign
  5. Mar 31, 2009 #4


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    Homework Helper

    Yes you can do that too. But understanding what happens to the function when you multiply it by a negative constant would be a useful tool to have in your arsenal :wink:
  6. Apr 1, 2009 #5


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    As you say, the zeroes are -2.5, 1, and 7. Suppose x< -2.5. Then each of the factors is negative. Since there are 4 factors, counting the '-2', there product, and the function value, is positive. Now take x between -2.5 and 1. The single factor (2x+ 5)= -2(x- 2.5) changes sign so there are now three negative factors: the function value is negative between -2.5 and 1. Take x between 1 and 7. Now the x-1 factor changes sign to postive and there are now 2 negative factors: the function value is positive between 1 and 7. Finally, if x> 7, all factors except the '-2' are positive: for x> 7, the function value is negative.
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