Solve inequalities with a polynomial of degree 3 or more

Grade 11 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Ari notices a squared factor in (x − 2)²(x + 3) > 0. Which x-values solve the inequality?

   • x < -3
   • x < -3 or x > 2
   • x ≥ -3
   • -3 < x < 2 or x > 2
2. 2.

   Bo notices a squared factor in (x + 1)²(x − 4) ≤ 0. Which x-values solve the inequality?

   • x ≤ 4
   • x < -1 or -1 < x < 4
   • -1 ≤ x ≤ 4
   • x = -1 or x ≥ 4
3. 3.

   Jun notices a squared factor in (x − 1)²(x + 2)(x − 5) ≥ 0. Which x-values solve the inequality?

   • -2 ≤ x ≤ 5
   • x ≤ -2 or x = 1 or x ≥ 5
   • x < -2 or x > 5
   • -2 ≤ x ≤ 1 or x ≥ 5
4. 4.

   Kira sees that x⁴ − 10x² + 9 factors like a quadratic in x². Which x-values solve x⁴ − 10x² + 9 < 0?

   • 1 < x < 3
   • -3 < x < -1 or 1 < x < 3
   • -3 ≤ x ≤ -1 or 1 ≤ x ≤ 3
   • x < -3 or -1 < x < 1 or x > 3
5. 5.

   Luz sees that x⁴ − 5x² + 4 factors like a quadratic in x². Which x-values solve x⁴ − 5x² + 4 ≥ 0?

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

   Milo sees that x⁴ − 13x² + 36 factors like a quadratic in x². Which x-values solve x⁴ − 13x² + 36 ≤ 0?

   • 2 ≤ x ≤ 3
   • x ≤ -3 or -2 ≤ x ≤ 2 or x ≥ 3
   • -3 ≤ x ≤ -2 or 2 ≤ x ≤ 3
   • -3 < x < -2 or 2 < x < 3
7. 7.

   Noah sees that x⁴ − 17x² + 16 factors like a quadratic in x². Which x-values solve x⁴ − 17x² + 16 > 0?

   • -4 < x < -1 or 1 < x < 4
   • x ≤ -4 or -1 ≤ x ≤ 1 or x ≥ 4
   • x < 1 or x > 4
   • x < -4 or -1 < x < 1 or x > 4
8. 8.

   Ren solves x³ ≤ 9x with a sign chart. Which x-values make x³ ≤ 9x true?

   • -3 ≤ x ≤ 3
   • -3 ≤ x ≤ 0 or x ≥ 3
   • x ≤ -3 or 0 ≤ x ≤ 3
   • x < -3 or 0 < x < 3
9. 9.

   Tala solves x³ + 8x < 6x² with a sign chart. Which x-values make x³ + 8x < 6x² true?

   • 2 < x < 4
   • 0 < x < 2 or x > 4
   • x < 0 or 2 < x < 4
   • x ≤ 0 or 2 ≤ x ≤ 4
10. 10.

    Zee solves x³ ≥ 16x with a sign chart. Which x-values make x³ ≥ 16x true?

    • -4 < x < 0 or x > 4
    • x ≤ -4 or 0 ≤ x ≤ 4
    • x ≤ -4 or x ≥ 4
    • -4 ≤ x ≤ 0 or x ≥ 4