Solve inequalities with a polynomial of degree 3 or more

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari starts a sign chart for f(x) = (x + 2)(x − 1)(x − 3). Separating them with commas, what are all the zeros of f?

   -2, 1, 3
2. 2.

   Bo starts a sign chart for f(x) = (x + 4)(x + 1)(x − 2). Separating them with commas, what are all the zeros of f?

   -4, -1, 2
3. 3.

   Esme starts a sign chart for f(x) = x(x + 5)(x − 2). Separating them with commas, what are all the zeros of f?

   -5, 0, 2
4. 4.

   Jun starts a sign chart for f(x) = x(x − 4)(x + 1). Separating them with commas, what are all the zeros of f?

   -1, 0, 4
5. 5.

   Kira tests one number in each interval of a sign chart for f(x) = (x + 3)(x − 1)(x − 5). What is f(4)?

   -21
6. 6.

   Luz tests one number in each interval of a sign chart for f(x) = (x + 2)(x − 3)(x − 6). What is f(-1)?

   28
7. 7.

   Milo tests one number in each interval of a sign chart for f(x) = (x + 4)(x + 1)(x − 2). What is f(-3)?

   10
8. 8.

   Noah tests one number in each interval of a sign chart for f(x) = (x + 5)(x − 2)(x − 4). What is f(3)?

   -8
9. 9.

   Pia finished the sign chart shown for f(x) = (x + 2)(x − 1)(x − 3). Which x-values make f(x) > 0?

   • x < -2 or 1 < x < 3
   • -2 ≤ x ≤ 1 or x ≥ 3
   • x < -2 or x > 3
   • -2 < x < 1 or x > 3
10. 10.

    Ren finished the sign chart shown for f(x) = (x + 4)(x − 1)(x − 5). Which x-values make f(x) ≤ 0?

    • -4 ≤ x ≤ 1 or x ≥ 5
    • -4 ≤ x ≤ 5
    • x ≤ -4 or 1 ≤ x ≤ 5
    • x < -4 or 1 < x < 5