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Math Help - Factor this beast.. Tricky Question

  1. #1
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    Factor this beast.. Tricky Question

    In Canada, hundreds of thousands of Cubic metres of wood are harvested each year. The function

    f(x)=1135x^4-8197x^3+15868x^2-2157x+176608 0<=x<=4

    models the harvested volume from 1993 to 1997

    Estimate the interval when less than 185000m^3 were harvested.

    So I setup the equation being <185000

    I brought the 185000 over and ended up with

    1135x^4-8197x^3+15868x^2-2157x-8392<0

    I can't find a factor using factor theorum, maybe i'm not trying hard enough but i've spent quite a bit on it. Could anyone assist?
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  2. #2
    Senior Member pacman's Avatar
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    Your Teacher surely will give you an integer solution. . . . .

    Given: f(x)=1135x^4-8197x^3+15868x^2-2157x+176608 0<=x<=4

    1135x^4-8197x^3+15868x^2-2157x-8392<0

    why not substitute those values above? Please have a try on these . . . .

    1) 1135x^4-8197x^3+15868x^2-2157x-8392 < 0, @ x = 0,

    2) 1135x^4-8197x^3+15868x^2-2157x-8392 < 0, @ x = 1,

    3) 1135x^4-8197x^3+15868x^2-2157x-8392 < 0, @ x = 2,

    4) 1135x^4-8197x^3+15868x^2-2157x-8392 < 0, @ x = 3,

    5) 1135x^4-8197x^3+15868x^2-2157x-8392 < 0, @ x = 4.

    surely more than one of them will satisfy your given equation . . . . please try. Below is a plot of your inequality - 1135x^4-8197x^3+15868x^2-2157x-8392<0.



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  3. #3
    MHF Contributor
    Grandad's Avatar
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    Hello Pankie

    Welcome to Math Help Forum
    Quote Originally Posted by Pankie View Post
    In Canada, hundreds of thousands of Cubic metres of wood are harvested each year. The function

    f(x)=1135x^4-8197x^3+15868x^2-2157x+176608 0<=x<=4

    models the harvested volume from 1993 to 1997

    Estimate the interval when less than 185000m^3 were harvested.

    So I setup the equation being <185000

    I brought the 185000 over and ended up with

    1135x^4-8197x^3+15868x^2-2157x-8392<0

    I can't find a factor using factor theorum, maybe i'm not trying hard enough but i've spent quite a bit on it. Could anyone assist?
    Unless you've been told to look for factors, I think that the clue is the word 'Estimate', which probably indicates that a numerical/graphical method is required. I don't know what tools you are allowed to use, but if you have a calculator or spreadsheet that will produce a graph, you'll get something like the one I've attached.

    This gives the interval (approximately) [0, 1.2] \cup [2.8,3.8].

    Grandad
    Attached Thumbnails Attached Thumbnails Factor this beast.. Tricky Question-untitled.jpg  
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  4. #4
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    Thanks for the responses. We are not permitted to use graphing calculators. I have tried all of the solutions you listed and none of them satisfy the equation.

    I guess im stuck
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