Factor by grouping

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Milo groups 2x³ + 8x² + 3x + 12 as (2x³ + 8x²) + (3x + 12). Type powers like x^2. What is the GCF of the first pair?

   2x^2
2. 2.

   Noah splits 3x³ + 15x² + 2x + 10 into two pairs, (3x³ + 15x²) and (2x + 10). Type powers like x^2. What is the GCF of the first pair?

   3x^2
3. 3.

   Ren starts grouping 5x³ + 30x² + x + 6 with the pair 5x³ + 30x². Type powers like x^2. What is the GCF of that pair?

   5x^2
4. 4.

   Tala groups 3x³ + 12x² + 5x + 20 as 3x²(x + ▢) + 5(x + ▢). What number goes in both boxes?

   4
5. 5.

   Zee writes 2x³ + 10x² + 3x + 15 = 2x²(x + ▢) + 3(x + ▢). What number goes in both boxes?

   5
6. 6.

   Ari draws 2x³ + 12x² + 7x + 42 as two rectangles: 2x²(x + ▢) + 7(x + ▢). What number goes in both boxes?

   6
7. 7.

   Bo needs the shared side: 3x³ + 21x² + 2x + 14 = 3x²(x + ▢) + 2(x + ▢). What number goes in both boxes?

   7
8. 8.

   Jun has reached 2x²(x + 3) + 5(x + 3), the grouped form of 2x³ + 6x² + 5x + 15. Which shows it as one product?

   • 2x²(x + 3) + 5(x + 3)
   • (x + 3)(x + 3)(2x² + 5)
   • (x + 3)(10x²)
   • (x + 3)(2x² + 5)
9. 9.

   Kira draws x²(x + 6) + 2(x + 6) as two rectangles with a shared side. Which shows x³ + 6x² + 2x + 12 as one product?

   • x²(x + 6) + 2(x + 6)
   • (x + 6)(x² + 2)
   • (x + 6)(2x²)
   • (x + 6)(x + 6)(x² + 2)
10. 10.

    Luz is one step from done: 3x³ + 3x² + 4x + 4 = 3x²(x + 1) + 4(x + 1). Which shows it as one product?

    • 3x²(x + 1) + 4(x + 1)
    • (x + 1)(12x²)
    • (x + 1)(x + 1)(3x² + 4)
    • (x + 1)(3x² + 4)