Factor completely: choose the method

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Kira factors 4x³ − 36x for a puzzle card. Which answer is factored completely?

   • 4x(x − 3)²
   • (2x − 6)(2x² + 6x)
   • 4x(x² − 9)
   • 4x(x − 3)(x + 3)
2. 2.

   Luz and three friends each factor 3x³ + 18x² + 27x. Which answer is factored completely?

   • (3x + 9)(x² + 3x)
   • 3x(x² + 6x + 9)
   • 3(x³ + 6x² + 9x)
   • 3x(x + 3)²
3. 3.

   Milo wants 2x³ − 8x² − 42x factored all the way. Which answer is factored completely?

   • (2x − 14)(x² + 3x)
   • 2(x³ − 4x² − 21x)
   • 2x(x² − 4x − 21)
   • 2x(x − 7)(x + 3)
4. 4.

   Pia factors 2x² − 72 completely as 2(x − ▢)(x + ▢). The same number goes in both boxes. What is that number?

   6
5. 5.

   Tala factors 6x² − 150 completely as 6(x − ▢)(x + ▢). The same number goes in both boxes. What is that number?

   5
6. 6.

   Zee factors 4x² − 256 completely as 4(x − ▢)(x + ▢). The same number goes in both boxes. What is that number?

   8
7. 7.

   Ari wants to factor 2x³ − 50x completely. Which step should come first?

   • Take out 2 only
   • Take out the GCF, 2x
   • Use the difference of squares right away
   • It cannot be factored
8. 8.

   Bo has 3x³ − 12x to factor completely. Which step comes first?

   • Use the difference of squares right away
   • Take out the GCF, 3x
   • Take out 3 only
   • It cannot be factored
9. 9.

   Esme wants to factor 4x² − 25 completely. Which step should come first?

   • Find two numbers that multiply to −25 and add to 4
   • Use the difference of squares
   • It cannot be factored
   • Take out the GCF, 2
10. 10.

    Jun gets 9x² − 64 on a puzzle card. Which step comes first to factor it completely?

    • Use the difference of squares
    • Take out the GCF, 3
    • It cannot be factored
    • Take out the GCF, x