Question 94415
End behavior
The highest power term determines what happens as x goes to + or to - infinity.
Since x^4 goes to  + infinity as x does, f(x) goes to + infinity.
Since x^4 goes to + infinity as x goes to - infinity, f(x) goes to + infinity.
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where cross the x axis
If touches the x axis at x=4 and at x=-2 but does not cross it.

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factors:
f(x) = x^4 + 12x^3 + 52x^2 +96x +64
f(x) = (x+2)^2 * (x+4)^2
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Cheers,
Stan H.