Results 1 to 9 of 9

Math Help - Find the zeros

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    54

    Find the zeros

    Find all the zeros of the function and write the polynomial as a product of linear factors.
    g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64 - 32

    So this looks extremely confusing, but I think that I have to use synthetic division. I'm not sure though. Can you help me please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by tsmith View Post
    Find all the zeros of the function and write the polynomial as a product of linear factors.
    g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64 - 32

    So this looks extremely confusing, but I think that I have to use synthetic division. I'm not sure though. Can you help me please?

    Check out the rational zero theorem here:

    3.3 - Real Zeros of Polynomial Functions
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    Quote Originally Posted by tsmith View Post
    Find all the zeros of the function and write the polynomial as a product of linear factors.
    g(x) = x^5 - 8x^4 + 28x^3 - 56x^2 + 64 - 32
    So this looks extremely confusing, but I think that I have to use synthetic division. I'm not sure though. Can you help me please?
    Hint: 2 is a triple root.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2009
    Posts
    54
    What exactly does that mean, if you don't mind?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by tsmith View Post
    What exactly does that mean, if you don't mind?
    (x-2)^3 is a factor of g(x)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by tsmith View Post
    What exactly does that mean, if you don't mind?
    That (x-2) is a triple zero.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Sep 2009
    Posts
    54
    So I would use 2 in the syntehtic division process?
    Thanks for answering, by the way
    Follow Math Help Forum on Facebook and Google+

  8. #8
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by tsmith View Post
    So I would use 2 in the syntehtic division process?
    Thanks for answering, by the way
    Yes, three consequtive times.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    x^5 - 8x^4 + 28x^3 - 56x^2 + 64x - 32 = (x - 2)^3(x^2 - 2x + 4)

    This one is irreducible (x^2 - 2x + 4).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find Zeros
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 12th 2010, 12:39 PM
  2. Find all zeros of...
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 18th 2010, 06:10 PM
  3. find the zeros of...
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 18th 2010, 12:55 PM
  4. Find all the Zeros
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: November 14th 2009, 04:45 PM
  5. Find All Zeros
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 22nd 2009, 10:54 AM

Search Tags


/mathhelpforum @mathhelpforum