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ap algebra

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Can you please help me with these problems I don't understand them? thanxs!

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero.

f(x) = 2(x - 2)(x + 4)^4
2(0-2)(0+4)^4 that's all I know

f(x) = 3(x - 3)(x - 6)^3

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

  • ap algebra -

    Take the first one:
    the first zero is at x=2 (it makes the first term zero) the second zero is at x=-4

    Now, for crossing the x axis (does the function change sign..take the x-2 term. If x <2, it is negative, if x>2, it is positive, so the function must cross the x axis at x=2. If it didn't change signs (check the (x+4)^4 term)), it much touch the x axis.

    I will be happy to critique your thinking.

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