Rational Root Theorem Practice

Directions: Which of the following lists contains all possible rational roots for the polynomial f(x) = 2x³ - 9x² + x + 12?

• ±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, ±6/2, ±12/2

• ±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, ±4/2, ±6/2, ±12/2

• ±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, ±6, ±12

• ±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2, ±4, ±6

Tags

CCSS.HSA.APR.B.2

Directions: Find the possible rational roots for the polynomial f(x) = x³ + 4x² - 11x - 30. Which of the following lists contains all possible rational roots?

• ±1, ±2, ±3, ±5, ±6, ±10, ±15, ±30

• ±1, ±2, ±3, ±4, ±5, ±6, ±11, ±30

• ±1, ±2, ±3, ±5, ±6, ±10, ±15, ±20

• ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15

Directions: Find the possible rational roots for the polynomial f(x) = 3x³ + 10x² - 27x - 36.

• ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36, ±1/3, ±2/3, ±4/3, ±6/3, ±12/3, ±18/3, ±36/3

• ±1, ±2, ±3, ±6, ±9, ±18, ±27, ±36, ±1/2, ±3/2, ±6/2, ±9/2, ±18/2, ±27/2, ±36/2

• ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±36, ±1/4, ±2/4, ±3/4, ±6/4, ±12/4, ±24/4, ±36/4

• ±1, ±2, ±3, ±5, ±10, ±15, ±30, ±1/3, ±2/3, ±5/3, ±10/3, ±15/3, ±30/3

Directions: Which of the following lists contains all possible rational roots for the polynomial f(x) = 4x³ - 7x² + 5x - 20?

• ±1, ±2, ±4, ±5, ±10, ±20, ±1/4, ±5/4, ±10/4, ±20/4

• ±1, ±2, ±4, ±5, ±7, ±20, ±1/4, ±2/4, ±5/4, ±7/4

• ±1, ±2, ±4, ±5, ±10, ±20, ±1/2, ±5/2, ±10/2, ±20/2

• ±1, ±2, ±4, ±5, ±10, ±20, ±1/7, ±5/7, ±10/7, ±20/7

Tags

CCSS.HSA.APR.B.2

Directions: Find the possible rational roots for the polynomial f(x) = 5x³ + 3x² - 8x - 24.

• ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/24, ±2/24, ±3/24, ±4/24, ±6/24, ±8/24, ±12/24

• ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/8, ±2/8, ±3/8, ±4/8, ±6/8, ±12/8, ±24/8

• ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/3, ±2/3, ±3/3, ±4/3, ±6/3, ±8/3, ±12/3, ±24/3

• ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/5, ±2/5, ±3/5, ±4/5, ±6/5, ±8/5, ±12/5, ±24/5

Directions: Which of the following lists contains all possible rational roots for the polynomial f(x) = 6x³ - 13x² + 7x + 14?

• ±1, ±2, ±3, ±6, ±7, ±14, ±1/13, ±2/13, ±3/13, ±6/13, ±7/13, ±14/13

• ±1, ±2, ±3, ±6, ±7, ±14, ±1/7, ±2/7, ±3/7, ±6/7, ±14/7

• ±1, ±2, ±3, ±6, ±7, ±14, ±1/6, ±2/6, ±3/6, ±7/6, ±14/6

• ±1, ±2, ±7, ±14, ±1/6, ±2/6, ±7/6, ±14/6

Which of the following lists all possible rational roots for the polynomial f(x) = 4x³ + x² - 25x + 21?