SOLUTION: Show that x = 1 is the only rational root for the polynomial f(x) = x^3 - 5x^2 +5x

SOLUTION: Show that x = 1 is the only rational root for the polynomial f(x) = x^3 - 5x^2 +5x - 1.

Question 923140: Show that x = 1 is the only rational root for the polynomial f(x) = x^3 - 5x^2 +5x - 1.
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Test 1 as a possible root of f(x) using synthetic division. Remainder 0 means root; otherwise, not root. Using Rational Roots Theorem, 1 is the ONLY possible root.

________1____|_____1_____ -5_______ 5________ -1
_____________|
_____________|____________1________-4__________1
_____________|_______________________________________
__________________1______-4_________1_________0

1 is a root of f(x), and it is the only rational root.
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