1. Let's state the problem: We want to find the factors of the polynomial $$x^3 + x^2 - 10x + 8$$. 2. The Rational Root Theorem tells us that any rational root of a polynomial with integer coefficients is a fraction $$\frac{p}{q}$$ where $$p$$ divides the constant term and $$q$$ divides the leading coefficient. 3. Here, the leading coefficient is 1, so $$q = 1$$. The constant term is 8, so possible values for $$p$$ are the factors of 8: $$\pm1, \pm2, \pm4, \pm8$$. 4. Because $$q=1$$, the possible rational roots are just the factors of 8: $$\pm1, \pm2, \pm4, \pm8$$. 5. We test these values by substituting into the polynomial to find which are roots. 6. This is why we only find factors for 8 when looking for rational roots of this polynomial: the Rational Root Theorem restricts possible rational roots to factors of the constant term divided by factors of the leading coefficient. 7. To summarize, since the leading coefficient is 1, the possible rational roots are exactly the factors of 8. Final answer: The possible rational roots to test are $$\pm1, \pm2, \pm4, \pm8$$.