Factor sums and differences of cubes, and higher-degree polynomials

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   On a worksheet, Luz factors 2x⁴ − 54x completely. Which answer is right?

   • (x − 3)(x² + 3x + 9)
   • 2x(x − 3)(x² + 3x + 9)
   • 2x(x − 3)(x² − 3x + 9)
   • 2x(x³ − 27)
2. 2.

   Noah factors 4x³ − 500 completely in pencil. Which answer is right?

   • 4(x − 5)(x² + 5x + 25)
   • 4(x − 5)(x² − 5x + 25)
   • 4(x³ − 125)
   • (x − 5)(x² + 5x + 25)
3. 3.

   On a puzzle card, Pia must factor x⁵ + 64x² completely. Which answer is right?

   • x²(x³ + 64)
   • (x + 4)(x² − 4x + 16)
   • x²(x + 4)(x² + 4x + 16)
   • x²(x + 4)(x² − 4x + 16)
4. 4.

   In a notebook, Tala writes x³ − 64y³ as (x − 4y) times a quadratic. Type powers like y^2. What is the quadratic?

   x^2 + 4xy + 16y^2
5. 5.

   Zee factors 125x³ − 8y³ in pencil. One factor is 5x − 2y. What is the other factor?

   25x^2 + 10xy + 4y^2
6. 6.

   On a puzzle card, 64x³ + y³ = (4x + y)( ? ). Esme needs the second factor. What is it?

   16x^2 - 4xy + y^2
7. 7.

   On a worksheet, Jun factors x⁴ + 2x³ − 8x − 16 completely by grouping. Which answer is right?

   • (x + 2)(x − 2)(x² − 2x + 4)
   • (x + 2)(x³ + 8)
   • (x + 2)(x³ − 8)
   • (x + 2)(x − 2)(x² + 2x + 4)
8. 8.

   In a notebook, Kira groups the four terms of x⁴ − 3x³ + 27x − 81 and keeps factoring. Which answer is fully factored?

   • (x − 3)(x + 3)(x² + 3x + 9)
   • (x − 3)(x³ + 27)
   • (x − 3)(x³ − 27)
   • (x − 3)(x + 3)(x² − 3x + 9)
9. 9.

   Luz factors x⁴ + x³ − 64x − 64 completely in pencil. Which answer is right?

   • (x + 1)(x − 4)(x² − 4x + 16)
   • (x + 1)(x³ − 64)
   • (x + 1)(x³ + 64)
   • (x + 1)(x − 4)(x² + 4x + 16)
10. 10.

    On a puzzle card, Milo must factor 2x⁴ − 5x³ + 16x − 40 completely. Which answer is right?

    • (2x − 5)(x³ − 8)
    • (2x − 5)(x + 2)(x² − 2x + 4)
    • (2x − 5)(x³ + 8)
    • (2x − 5)(x + 2)(x² + 2x + 4)