x^3 + 3x^2 - 2x - 75 = 0
75 factors into 3 * 5 * 5.
Things you can make with those factors: 3, 5, 15, 25, 75
If x = 3 then. . . 27 + 27 - 6 - 75 = not 0
If x = 5 then 125 + 75 - 10 - 75 = not 0
If x = -3 then -27 + 27 + 6 - 75 = not 0
If x = -5 then -125 + 75 + 10 - 75 = not 0
15, -15, 25, -25, 75, and -75 will be completely dominated by the x^3, so they won't = 0
1 and -1 would be dominated by the 75, so they won't = 0
This equation does not appear to have any rational (whole number or fraction) roots.
If you put the equation in here ( http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php ) you'll see that it does have one irrational (but real) root and two complex (and irrational) roots. I don't think, in Algebra 1, these would be something you would be expected to deal with. You're not far enough long in math to mess with things like complex math (math using square roots of negative numbers) yet.