Remainder and factor theorems

Question 1

Find the remainder when x³ − 2x² − 5x + 6 is divided by (x − 1).

Answer 

Question 2

(x − 3) is a factor of x³ − 7x − 6. Solve x³ − 7x − 6 = 0. Give all three solutions, separated by commas.

x = 

Question 3

Find the remainder when x³ − 6x² + 5x − 2 is divided by (x − 2).

Answer 

Question 4

(x + 1) is a factor of x³ + 4x² − x − 4. Solve x³ + 4x² − x − 4 = 0. Give all three solutions, separated by commas.

x = 

Question 5

Find the remainder when x³ − 5x² + 2x − 2 is divided by (x − 1).

Answer 

Question 6

(x + 1) is a factor of x³ + 4x² − x − 4. Solve x³ + 4x² − x − 4 = 0. Give all three solutions, separated by commas.

x = 

Question 7

Find the remainder when x³ + x² − 5x − 7 is divided by (x − 3).

Answer 

Question 8

(x + 5) is a factor of x³ − 2x² − 23x + 60. Solve x³ − 2x² − 23x + 60 = 0. Give all three solutions, separated by commas.

x = 

Question 9

Find the remainder when x³ + 3x² − 9x + 9 is divided by (x + 2).

Answer 

Question 10

(x − 3) is a factor of x³ − x² − 14x + 24. Solve x³ − x² − 14x + 24 = 0. Give all three solutions, separated by commas.

x = 

Question 11

Find the remainder when x³ − 6x² − 6x + 4 is divided by (x + 3).

Answer 

Question 12

(x − 2) is a factor of x³ + 3x² − 4x − 12. Solve x³ + 3x² − 4x − 12 = 0. Give all three solutions, separated by commas.

x = 

Question 13

Find the remainder when x³ + 4x² + 6x − 11 is divided by (x − 1).

Answer 

Question 14

(x − 3) is a factor of x³ − x² − 9x + 9. Solve x³ − x² − 9x + 9 = 0. Give all three solutions, separated by commas.

x = 

Question 15

Find the remainder when x³ + 2x² + 2x − 3 is divided by (x + 2).

Answer 

Question 16

(x + 1) is a factor of x³ + 10x² + 29x + 20. Solve x³ + 10x² + 29x + 20 = 0. Give all three solutions, separated by commas.

x =