Find all the zeroes of the polynomial function f (x) = x^3 - 5x^2 + 6x - 30.

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What I like to in these problems is the grouping method. Split it into x^3-5x^2 ... 6x-30. Then factor so x^2 (x-5) and 6 (x-5). Now that both are factored put the coefficients together and use (x-5). This means that you have (x^2+6) and (x-5). Solve and your zeroes are + and - root 6 and 5.