Potential roots of p(x) = x^4 - 9x^2 - 4x + 12

-6, -4, -3, -2, -1, 1, 2, 3, 4, 6

Step-by-step explanation:

The general formula for a fourth-degree polynomial is

f(x) = ax⁴ + bx³ + cx² + dx + e

Your polynomial is  

f(x) = x⁴ - 9x² - 4x + 12

a = 1; e = 12

According to the Rational Roots Theorem, the possible rational roots are the factors of e divided by the factors of a.

Factors of e = ±1, ±2, ±3, ±4, ±6

Factors of a = ±1

Potential roots are x = ±1 ±2, ±3, ±4 ± 6

Putting them in order, we get the potential roots

x = -6, -4, -3, -2, -1, 1, 2, 3, 4, 6

(The graph of your function shows roots at x = -2, x = 1, and x = 3.)