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Math Help - Leading ciefficient test

  1. #1
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    Leading ciefficient test

    Use the leading coefficient test to indicate the end behavior of the graph of the polynomial function. Indicate the zero of the function.

    f(x)=-2x^3(x+5)^4(x-3)^2

    I need help with this problem. I don't even know where to begin.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok

    Quote Originally Posted by theevilp0ptart View Post
    Use the leading coefficient test to indicate the end behavior of the graph of the polynomial function. Indicate the zero of the function.

    f(x)=-2x^3(x+5)^4(x-3)^2

    I need help with this problem. I don't even know where to begin.
    Is this supposed to be f(x)=-2x^3\cdot(x+5)^4\cdot(x-3)^2?
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  3. #3
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    Quote Originally Posted by Mathstud28 View Post
    Is this supposed to be f(x)=-2x^3\cdot(x+5)^4\cdot(x-3)^2?
    Yes.
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  4. #4
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    Quote Originally Posted by theevilp0ptart View Post
    Use the leading coefficient test to indicate the end behavior of the graph of the polynomial function. Indicate the zero of the function.

    f(x)=-2x^3(x+5)^4(x-3)^2

    I need help with this problem. I don't even know where to begin.
    So the degree of f(x) is p and the lead terms will be of the form

    -2x^9 (why?)

    as x \to -\infty \mbox{  f(x) } \to \infty

    as x \to \infty \mbox{  f(x) } \to -\infty

    again why?

    Since it is already factored the zero's are x=0,-5,3

    Good luck.
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  5. #5
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    Quote Originally Posted by TheEmptySet View Post
    So the degree of f(x) is p and the lead terms will be of the form

    -2x^9 (why?)

    as x \to -\infty \mbox{  f(x) } \to \infty

    as x \to \infty \mbox{  f(x) } \to -\infty

    again why?

    Since it is already factored the zero's are x=0,-5,3

    Good luck.
    I do not understand why it would be -2x^9
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  6. #6
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    Quote Originally Posted by theevilp0ptart View Post
    I do not understand why it would be -2x^9
    What would happen if we multiplied out the whole thing?

    Lets look at one part

    (x+5)^4=(x+5)(x+5)(x+5)(x+5)

    We distributedthe whole thing out (we don't need to) to find the highest power of x .

    Well to get that terms we would multiply x by x by x by x =x^4

    <br />
f(x)=-2x^3 \cdot \underbrace{(x+5)^4}_{x^4} \cdot \underbrace{(x-3)^2}_{x^2}<br />

    so our lead term will be -2x^9
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