For the polynomial function below: (a) List each real zero and its multiplicity.

Question

For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the x-axis at each x-intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior, that is, find the power function that the graph of f resembles for large values of |x|. f(x) = (x - 6)^3 (x + 9)^2 Find any real zeros of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The real zero(s) of f is/are. (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answer as needed.) There are no real zeros. The multiplicity of the larger zero is. (Type a whole number.) The multiplicity of the smaller zero is .

Explanation / Answer

Real zeros : x=-9 and x=6

Multiplicity of larger zero=3

Multiplicity of smaller zero=2

If the degree of any polynomial is n, then maximum no of turning point will be (n-1). The equeation in question is polynomial of degree 5 and hence maximu number of turning point will be (5-1)=4

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