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Math Help - I NEED MAJOR HELP!(Question on Polynomials)

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    I NEED MAJOR HELP!(Question on Polynomials)

    Ok so this is my tips question which is due tomorrow for marks and I havnt been able to think how to do it.

    The Volume of a cylindrical can is
    4(pi)x^3 + 28(pi)x^2 + 65(pi)x + 50(pi) cm^3. If the can has a height of
    (x +2)cm, what is the radius of the cylinder? Now so far I figured the way to figure this out is to take the formula for Volume of a cylinder which is V=pi*r^2 *h and rearange is so your solving for r^2 instead so it would be r^2=(pi)(h)(V). The problem is im pretty sure I need to factor that equation out or expand w/e it is. I know how to expand out an equation where theres just x2 + x + 0 lets say but I dont know how to expand it when you have that extra x so its now x3 + x2 + x + 0. Can someone plz help me right now whoever's on at this time? Thanks!
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    Quote Originally Posted by zarlock99 View Post
    Ok so this is my tips question which is due tomorrow for marks and I havnt been able to think how to do it.

    The Volume of a cylindrical can is
    4(pi)x^3 + 28(pi)x^2 + 65(pi)x + 50(pi) cm^3. If the can has a height of
    (x +2)cm, what is the radius of the cylinder? Now so far I figured the way to figure this out is to take the formula for Volume of a cylinder which is V=pi*r^2 *h and rearange is so your solving for r^2 instead so it would be r^2=(pi)(h)(V). The problem is im pretty sure I need to factor that equation out or expand w/e it is. I know how to expand out an equation where theres just x2 + x + 0 lets say but I dont know how to expand it when you have that extra x so its now x3 + x2 + x + 0. Can someone plz help me right now whoever's on at this time? Thanks!
    V = \pi r^2 h

    \Rightarrow r^2 = \frac V{\pi h} = \frac {4x^3 + 28x^2 + 65x + 50}{x + 2}

    now, do polynomial long division (or synthetic division) to find r^2, then square root both sides when done
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    But what happened to the pi's within the equation for the volume?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zarlock99 View Post
    But what happened to the pi's within the equation for the volume?
    i factored them out and canceled them with the \pi in the denominator
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    So when I use synthetic devision i get this
    x3 x2 x
    -2| 4 28 65 50
    -8 -40 -50
    _______________
    4 20 25 0 R=0

    So would that be 4x^3 + 20x^2 + 25x + 0? Then how so I take the square root of that?
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    By the way, the answer is supposed to be 2x + 5, I just need to know how to get that answer.
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    Quote Originally Posted by zarlock99 View Post
    So when I use synthetic devision i get this
    x3 x2 x
    -2| 4 28 65 50
    -8 -40 -50
    _______________
    4 20 25 0 R=0

    So would that be 4x^3 + 20x^2 + 25x + 0? Then how so I take the square root of that?
    no, you just divided, how would you end up with the same degree polynomial?

    the answer is 4x^2 + 20x + 25

    now take the square root of that and that is r
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    ooooooooo I see, iunno but for some reason when I was looking through my notes I thought I saw after using synthetic devision u still stick with the x3, x2, and x but it never made sence, now i does tho. Thanks man a lot, u just saved me from losing marks.
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    well actually its not completely resolved unless the answer that was given is wrong. When I square root that I get 2x + 4.47 + 5, I got the 4.47 by taking the square root of 20x, but the answer that was given is (2x + 5)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zarlock99 View Post
    well actually its not completely resolved unless the answer that was given is wrong. When I square root that I get 2x + 4.47 + 5, I got the 4.47 by taking the square root of 20x, but the answer that was given is (2x + 5)
    you cannot take square roots like that!



    anyway, you just foil: 4x^2 + 20x + 25 = (2x + 5)(2x + 5) = (2x + 5)^2

    so r^2 = (2x + 5)^2

    \Rightarrow r = 2x + 5
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