Factor completely: choose the method

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Kira factors x⁴ − 16 with two cuts in a row. Which answer is factored completely?

   • It cannot be factored
   • (x² + 4)(x² − 4)
   • (x² + 4)(x − 2)(x + 2)
   • (x − 2)(x + 2)(x − 2)(x + 2)
2. 2.

   Luz wants 16x⁴ − 1 factored all the way. Which answer is factored completely?

   • (2x − 1)(2x + 1)(2x − 1)(2x + 1)
   • It cannot be factored
   • (4x² + 1)(4x² − 1)
   • (4x² + 1)(2x − 1)(2x + 1)
3. 3.

   Milo takes out the GCF of 2x⁴ − 162 and keeps going. Which answer is factored completely?

   • 2(x² + 9)(x − 3)(x + 3)
   • 2(x⁴ − 81)
   • 2(x² + 9)(x² − 9)
   • 2(x − 3)(x + 3)(x − 3)(x + 3)
4. 4.

   Noah factors 3x⁴ − 48 for a challenge card. Which answer is factored completely?

   • 3(x − 2)(x + 2)(x − 2)(x + 2)
   • 3(x² + 4)(x² − 4)
   • 3(x² + 4)(x − 2)(x + 2)
   • 3(x⁴ − 16)
5. 5.

   Pia groups x³ + 2x² − 9x − 18 in pairs and keeps going. Which answer is factored completely?

   • (x + 2)(x² + 9)
   • (x + 2)(x − 3)²
   • (x + 2)(x² − 9)
   • (x + 2)(x − 3)(x + 3)
6. 6.

   Ren factors x³ − 5x² − 4x + 20 by grouping, then looks again. Which answer is factored completely?

   • (x − 5)(x² + 4)
   • (x − 5)(x − 2)²
   • (x − 5)(x − 2)(x + 2)
   • (x − 5)(x² − 4)
7. 7.

   Tala wants 2x³ + 3x² − 8x − 12 factored all the way. Which answer is factored completely?

   • (2x + 3)(x² + 4)
   • (2x + 3)(x² − 4)
   • (2x + 3)(x − 2)(x + 2)
   • (2x + 3)(x − 2)²
8. 8.

   Ari factors 6x² + 34x + 20 completely and gets 2(3x + 2)(x + ▢). It may be negative. What number goes in the box?

   5
9. 9.

   Bo factors 6x² − 9x − 60 completely and gets 3(2x + 5)(x + ▢). It may be negative. What number goes in the box?

   -4
10. 10.

    Jun factors 10x² − 46x + 24 completely and gets 2(5x − 3)(x + ▢). It may be negative. What number goes in the box?

    -4