Solve inequalities with a polynomial of degree 3 or more

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Ari factors f(x) = x³ − x² − 6x to start a sign chart. Separating them with commas, what are all the zeros of f?

   -2, 0, 3
2. 2.

   Bo factors f(x) = x³ + 2x² − 15x to start a sign chart. Separating them with commas, what are all the zeros of f?

   -5, 0, 3
3. 3.

   Esme factors f(x) = x³ − 7x² + 10x to start a sign chart. Separating them with commas, what are all the zeros of f?

   0, 2, 5
4. 4.

   Jun factors f(x) = x³ + x² − 4x − 4 to start a sign chart. Separating them with commas, what are all the zeros of f?

   -2, -1, 2
5. 5.

   Kira solves (x + 1)(x − 2)(x − 4) < 0 with a sign chart. Which x-values are the solution?

   • -1 < x < 2 or x > 4
   • x < -4 or -2 < x < 1
   • x ≤ -1 or 2 ≤ x ≤ 4
   • x < -1 or 2 < x < 4
6. 6.

   Milo solves (x + 3)(x − 1)(x − 4) ≥ 0 with a sign chart. Which x-values are the solution?

   • x ≤ -3 or x ≥ 4
   • -3 < x < 1 or x > 4
   • -4 ≤ x ≤ -1 or x ≥ 3
   • -3 ≤ x ≤ 1 or x ≥ 4
7. 7.

   Noah solves (x + 6)(x + 1)(x − 2) ≤ 0 with a sign chart. Which x-values are the solution?

   • -6 ≤ x ≤ 2
   • x < -6 or -1 < x < 2
   • x ≤ -6 or -1 ≤ x ≤ 2
   • -6 ≤ x ≤ -1 or x ≥ 2
8. 8.

   Pia must factor before making a sign chart. Which x-values solve x³ − 2x² − 8x ≥ 0?

   • -2 ≤ x ≤ 0 or x ≥ 4
   • x ≤ -2 or x ≥ 4
   • x ≤ -2 or 0 ≤ x ≤ 4
   • -2 < x < 0 or x > 4
9. 9.

   Ren must factor before making a sign chart. Which x-values solve x³ + x² − 12x < 0?

   • x < -4 or 0 < x < 3
   • x ≤ -4 or 0 ≤ x ≤ 3
   • -4 < x < 3
   • -4 < x < 0 or x > 3
10. 10.

    Zee must factor before making a sign chart. Which x-values solve x³ + 6x² + 5x ≤ 0?

    • -5 ≤ x ≤ -1
    • x < -5 or -1 < x < 0
    • x ≤ -5 or -1 ≤ x ≤ 0
    • -5 ≤ x ≤ -1 or x ≥ 0