4. [22 pts] For the function ?(?) = 2?5 ? 9?4 + 12?3 ? 12?2...

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4. [22 pts] For the function ?(?) = 2?5 ? 9?4 + 12?3 ? 12?2 +10? ? 3 answer the following:

a. [2 pts] Determine whether the function represents apolynomial. Justify your answer.

b. [4 pts] Determine whether the function satisfies theIntermediate Value Theorem on the interval [0, 5]. Justify youranswer.

c. [2 pts] Determine the number (quantity) of complex zeros thatthe function has, provided the each zero is counted by itsmultiplicity.

d. [4 pts] List all the possible rational zeros:

e. [2 pts] Use part (d) result and a calculator to find theactual rational zeros. List the zeros here:

{ ____________________ }

f. [4 pts] Use the previous result, synthetic division, longdivision, quadratic formula, or square root property to find allthe remaining zeros of f(x).

g. [4 pts] Use the previous result to rewrite f(x) as a productof linear factors.

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