Answer: b) ±1, ±2, ±7, ±14, ±1/3, ±2/3, ±7/3, ±14/3
Step-by-step explanation:
The possible rational roots are all of the factors of P (coefficient of last term) divided by each of the factors of Q (coefficient of first term).
-3x⁴ - 9x³ - 6x² - 8x + 14
[tex]\dfrac{P}{Q}=\dfrac{factors\ of\ 14}{factors\ of\ 3}=\pm \dfrac{1,2,7,14}{1,3}\\\\\\=\pm \bigg\{\dfrac{1}{1},\dfrac{2}{1},\dfrac{7}{1},\dfrac{14}{1}, \quad \dfrac{1}{3}, \dfrac{2}{3}, \dfrac{7}{3}, \dfrac{14}{3}\bigg\}\\\\\\=\pm \bigg\{1, 2, 7, 14, \quad \dfrac{1}{3}, \dfrac{2}{3}, \dfrac{7}{3}, \dfrac{14}{3}\bigg\}[/tex]
