Remainder and factor theorems

Question 1

(x + 5) is a factor of x³ + x² − 25x − 25. Solve x³ + x² − 25x − 25 = 0. Give all three solutions, separated by commas.

x = 

Question 2

Find the remainder when x³ − 5x² − 3x + 4 is divided by (x + 1).

Answer 

Question 3

(x − 4) is a factor of x³ − 4x² − 9x + 36. Solve x³ − 4x² − 9x + 36 = 0. Give all three solutions, separated by commas.

x = 

Question 4

Find the remainder when x³ + 3x² + 8x + 2 is divided by (x − 1).

Answer 

Question 5

(x − 5) is a factor of x³ − 19x − 30. Solve x³ − 19x − 30 = 0. Give all three solutions, separated by commas.

x = 

Question 6

Find the remainder when x³ + 5x² + 2x − 12 is divided by (x + 3).

Answer 

Question 7

(x − 4) is a factor of x³ − x² − 22x + 40. Solve x³ − x² − 22x + 40 = 0. Give all three solutions, separated by commas.

x = 

Question 8

Find the remainder when x³ + 5x² + 3x − 12 is divided by (x + 1).

Answer 

Question 9

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

x = 

Question 10

Find the remainder when x³ − 4x² − 9x + 11 is divided by (x − 1).

Answer 

Question 11

(x + 3) is a factor of x³ + 6x² + 11x + 6. Solve x³ + 6x² + 11x + 6 = 0. Give all three solutions, separated by commas.

x = 

Question 12

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

Answer 

Question 13

(x − 3) is a factor of x³ + 4x² − 11x − 30. Solve x³ + 4x² − 11x − 30 = 0. Give all three solutions, separated by commas.

x = 

Question 14

Find the remainder when x³ − 2x² − 5x + 12 is divided by (x − 1).

Answer 

Question 15

(x − 3) is a factor of x³ − 12x² + 47x − 60. Solve x³ − 12x² + 47x − 60 = 0. Give all three solutions, separated by commas.

x = 

Question 16

Find the remainder when x³ − 6x² + 5x + 7 is divided by (x + 2).

Answer