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Math Help - Polynomial functions

  1. #1
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    Polynomial functions

    Expand and simplify. Express equations in standard form.
    1. f(x) = -2(x-1)(x+4)(x+1)(x-3)
    2. f(x) = (x+2)(x+1)(x+4)
    3.f(x) = x(x-6)
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  2. #2
    Member SENTINEL4's Avatar
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    I'm not sure what you have to do... They seem in a pretty simple form. Maybe you want something like the following..
    3.f(x) = x(x-6)
    x(x-6) = x^2-6x = x^2-6x+9-9 = ( x^2-6x+9)-9 = (x-3)^2-9
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  3. #3
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    Quote Originally Posted by flwer_13 View Post
    Expand and simplify. Express equations in standard form.
    1. f(x) = -2(x-1)(x+4)(x+1)(x-3)
    2. f(x) = (x+2)(x+1)(x+4)
    3.f(x) = x(x-6)
    consider these general forms

    a(b+c) =ab+ac


    (a+b)(c+d) =ac+ad+bc+bd


    (a+b)(c+d)(e+f) =eac+ead+ebc+ebd+fac+fad+fbc+fbd


    (a+b)(c+d)(e+f)(g+h)

    =geac+gead+gebc+gebd+gfac+gfad+gfbc+gfbd

    +heac+head+hebc+hebd+hfac+hfad+hfbc+hfbd

    You must group like terms.
    Last edited by pickslides; May 11th 2009 at 03:59 PM. Reason: typo
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  4. #4
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    Quote Originally Posted by flwer_13 View Post
    Expand and simplify. Express equations in standard form.
    1. f(x) = -2(x-1)(x+4)(x+1)(x-3)
    For this one, note first that (x - 1)(x + 1) = x^2 - 1. Then multiply this by the product of the other two linear factors, x^2 + x - 12. Multiply that through by the -2, and you're done.

    Quote Originally Posted by flwer_13 View Post
    2. f(x) = (x+2)(x+1)(x+4)
    You can multiply the polynomial factors in any order you like, but it might be quickest to multiply the x + 2 by the x + 4, and then multiply the result by the x + 1.

    Quote Originally Posted by flwer_13 View Post
    3.f(x) = x(x-6)
    Take the x through the parentheses, and you're done.
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