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Math Help - Polynomial Functions

  1. #1
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    Polynomial Functions

    Can anyone help me solve this question..its urgent ^^ thank you

    For each of the following polynomial functions, determine if each of x=-1, x=0 and/or x=2 is a zero of the polynomial and, if so, whether its muliplicity is even or odd.

    1.) f(x)= x^4+2x^3+2x^2
    2.) g(x)=5x^2-5x-10
    3.) h(x)= x^3(x+1)^4(x+2)
    4.) The graph of p(x) is :
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lemontea View Post
    Can anyone help me solve this question..its urgent ^^ thank you

    For each of the following polynomial functions, determine if each of x=-1, x=0 and/or x=2 is a zero of the polynomial and, if so, whether its muliplicity is even or odd.

    1.) f(x)= x^4+2x^3+2x^2
    2.) g(x)=5x^2-5x-10
    3.) h(x)= x^3(x+1)^4(x+2)
    4.) The graph of p(x) is :
    multiplicity just tells you how many times a root is "repeated".

    for instance, if we had a quadratic of the form (x - 2)^2, the only root would be x = 2, since this makes the quadratic zero. but, a quadratic must have two roots. so there should be one more, but low and behold! the square tells us the root is repeated a second time. so x = 2 is a root with multiplicity 2

    note that f(x) = x^2 (x^2 + 2x + 2)

    what x's make this zero?


    note that g(x) = 5(x^2 - x - 2) = 5(x - 2)(x + 1)

    what x's make this zero?


    h(x) is already in a nice factored form, what x's make it zero? the powers tell you the multiplicity


    for p(x), look at the graph. wherever the graph touches the x-axis, that is a root. if it passes through, the multiplicity is 1, if there is a hump and the graph touches the x-axis without cutting it, the multiplicity is 2.
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