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The function given is:

\[ f(x) = 4x^5 - 18x^4 - 6x^3 + 91x^2 - 60x + 9 \]

To find all the zeros of this polynomial, we will apply various algebraic techniques including factoring and using numerical methods if necessary.

### Step 1: Factorization and Rational Root Theorem
We will first test for possible rational roots using the Rational Root Theorem. This theorem states that any rational solution \(\frac{p}{q}\), where \(p\) is a factor of the constant term and \(q\) is a factor of the leading coefficient, could be a root of the polynomial.

Let's check for rational roots and factor the polynomial accordingly.

Find all zeros of the polynomial: f(x) = 4x^5 - 18x^4 - 6x^3 + 91x^2 - 60x + 9

Discover how to find all zeros of the polynomial function f(x) = 4x^5 - 18x^4 - 6x^3 + 91x^2 - 60x + 9 using factorization and the Rational Root Theorem. This detailed solution is ideal for students in grades 11-12, covering advanced algebraic methods.

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