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.

   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
2. 2.

   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
3. 3.

   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
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

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

   • -2 ≤ x ≤ 1 or x ≥ 3
   • x < -2 or 1 < x < 3
   • -2 < x < 1 or x > 3
   • x < -2 or x > 3
8. 8.

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

   • x ≤ -4 or 1 ≤ x ≤ 5
   • x < -4 or 1 < x < 5
   • -4 ≤ x ≤ 1 or x ≥ 5
   • -4 ≤ x ≤ 5
9. 9.

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

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

    Zee finished the sign chart shown for f(x) = (x + 1)(x − 2)(x − 6). Which x-values make f(x) ≥ 0?

    • x ≤ -1 or 2 ≤ x ≤ 6
    • -1 ≤ x ≤ 2 or x ≥ 6
    • x ≤ -1 or x ≥ 6
    • -1 < x < 2 or x > 6