Common Core HSA.APR.B.3 worksheet

Question 1

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

Answer 

Question 2

f(x) = (x − 3)(x − 6)(x − 1). Find all the zeros of f, separated by commas.

x = 

Question 3

Solve x³ + 4x² − 5x = 0. Give all the solutions, separated by commas.

x = 

Question 4

(x − 1) is a factor of x³ + 7x² + 7x − 15. Solve x³ + 7x² + 7x − 15 = 0. Give all three solutions, separated by commas.

x = 

Question 5

x = −1 is a solution of x³ − 2x² − x + 2 = 0. Find all the solutions, separated by commas.

x = 

Question 6

Without solving, find the sum of the roots of 2x² − x + 5 = 0. Give a fraction if needed.

Answer (as a fraction)

Question 7

Describe the end behaviour of f(x) = x⁴ + 3x − 1.

• A. Up on the left, up on the right
• B. Down on the left, down on the right
• C. Down on the left, up on the right
• D. Up on the left, down on the right

Question 8

Write a quadratic x² + bx + c with roots 8 and −2. Type it.

Answer 

Question 9

Find the remainder when x³ + 6x² − 7x + 12 is divided by (x + 2).

Answer 

Question 10

f(x) = −(x − 5)(x − 4)(x + 3). Find all the zeros of f, separated by commas.

x = 

Question 11

Solve x³ + x² − 20x = 0. Give all the solutions, separated by commas.

x = 

Question 12

(x − 3) is a factor of x³ − 7x² + 7x + 15. Solve x³ − 7x² + 7x + 15 = 0. Give all three solutions, separated by commas.

x = 

Question 13

x = −4 is a solution of x³ − 16x = 0. Find all the solutions, separated by commas.

x = 

Question 14

Without solving, find the sum of the roots of 2x² + 3x + 5 = 0. Give a fraction if needed.

Answer (as a fraction)

Question 15

Describe the end behaviour of f(x) = x⁵ + 3x − 1.

• A. Up on the left, up on the right
• B. Down on the left, down on the right
• C. Down on the left, up on the right
• D. Up on the left, down on the right

Question 16

Write a quadratic x² + bx + c with roots 0 and −1. Type it.

Answer