Question 1143451
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{{{ x^3-8x^2+17x-4 = (x-4)(x^2-4x+1) }}}

[ In factor x-a  out from the polynomial, a must be a factor of -4: so +/-1, +/-2, and +/-4 are the choices. ]
That gets you the rational root x=4<br>

{{{ (x^2-4x+1) }}} factors to  {{{ (x - (sqrt(3)) - 2)(x + (sqrt(3)) - 2) }}}

which will give you the other roots.