Use the rational root theorem and the factor theorem to help solve the equation. x ³ - x ² - 65 x + 225 = 0 A){-9, 5} B){-5, 9} C){-8 , 3} D){-9, 3} E){-8, 5}

Question

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The given equation is $x^3 - x^2 - 65x + 225 = 0$. By applying the Rational Root Theorem, we look for factors of the constant term (225) and the leading coefficient (1). The factors of 225 are ±1, ±3, ±5, ±9, ±15, ±25, ±45, ±75, ±225. Testing these as possible roots, we find that x = -9 and x = 5 are roots of the equation, which can be verified by direct substitution or synthetic division. Thus, the correct answer is {-9, 5}.

Use the Rational Root Theorem and the Factor Theorem to Help