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Math Help - Writing Polynomial functions

  1. #1
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    Writing Polynomial functions

    hello I just started on these tonight and i understand all the terms but this one is tricky because it has to go through a specific point and i dont quite understand how to do it yet.

    Any help is appreciated:

    The polynomial of degree 4, has a root of multiplicity 2 at and roots of multiplicity 1 at and . It goes through the point .
    Find a formula for .

    My train of thought
    P(x)=
    (X-4)^2 Multiplicity of 2 and zeros at 4
    (X) Multiplicity of 1 and zero at 0
    (X+3) Multiplicity of 1 and zero at -3

    When i graph it, i get a 4th degree polynominal that goes through (-3,0)(0,0) and bounces off (4,0) but does not go through (5,24) instead it goes through (5,40).
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  2. #2
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    Quote Originally Posted by xsavethesporksx View Post
    hello I just started on these tonight and i understand all the terms but this one is tricky because it has to go through a specific point and i dont quite understand how to do it yet.

    Any help is appreciated:

    The polynomial of degree 4, has a root of multiplicity 2 at and roots of multiplicity 1 at and . It goes through the point .
    Find a formula for .

    My train of thought
    P(x)=
    (X-4)^2 Multiplicity of 2 and zeros at 4
    (X) Multiplicity of 1 and zero at 0
    (X+3) Multiplicity of 1 and zero at -3

    When i graph it, i get a 4th degree polynominal that goes through (-3,0)(0,0) and bounces off (4,0) but does not go through (5,24) instead it goes through (5,40).
    P(x) = kx(x+3)(x-4)^2

    P(5) = 24

    solve for k
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