Find all the zeros of x^3-5x^2-x+5

The fact that the coefficients are pairwise identical (except for sign) tells you that x^2 - 1 is a factor (and x-5 is the other factor). Of course, you recognize x^2-1 as a special form (the difference of squares) that is factored as (x + 1) (x - 1).

The zeros are x = - 1, + 1, + 5.

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A graphing calculator confirms this.