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Math Help - Prep Qs for test

  1. #1
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    Prep Qs for test

    -Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
    -3, -4 + i, 1-√3

    Factor Polynomial completely
    8c^3 - 512


    Evaluate Expression
    (1.5 x 10^4)(3.2 x 10^-8) <power of negative 8
    (1.2 x 10^-7) <power of negative 7

    -I could really use help on how to solve these. I have a test tomorrow and these are the main type of problems i didnt understand.
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  2. #2
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    Quote Originally Posted by Pineapple View Post
    -Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
    -3, -4 + i, 1-√3
    Linear factors are (z + 3), the conjugate pair (z + 4 - i) and (z + 4 + i) (since the conjugate root theorem is valid), and (z - 1 + \sqrt{3}). Therefore .....

    I was tempted to add (z - 1 - \sqrt{3}) as a factor so that z^2 - 2z - 2 is a quadratic factor and you have a nice simple polynomial, but then the resulting polynomial is not of least degree.


    Quote Originally Posted by Pineapple View Post
    Factor Polynomial completely
    8c^3 - 512
    = 8(c^3 - 64) = 8(c^3 - 4^3) and I'm sure you know how to factorise a difference of two cubes.

    Quote Originally Posted by Pineapple View Post
    Evaluate Expression
    (1.5 x 10^4)(3.2 x 10^-8) <power of negative 8
    (1.2 x 10^-7) <power of negative 7
    [snip]
    Both can be done using a calculator. What's actually required here? A technology free simplification (in which case nothing needs to be done with the second) .....?
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