Factor by grouping

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Noah writes x³ − 4x² − 7x + 28 as x²(x − 4) + ▢(x − 4). It may be negative. What number goes in the box?

   -7
2. 2.

   Pia wants both brackets to be x − 2: 3x³ − 6x² − 4x + 8 = 3x²(x − 2) + ▢(x − 2). It may be negative. What goes in the box?

   -4
3. 3.

   Ren groups 2x³ − 10x² − 3x + 15 as 2x²(x − 5) + ▢(x − 5). It may be negative. What number goes in the box?

   -3
4. 4.

   Tala splits 10x² + 23x + 12 into 10x² + 15x + 8x + 12. Grouped, it is 5x(2x + 3) + ▢(2x + 3). What number goes in the box?

   4
5. 5.

   Ari writes 12x² + 35x + 18 as 12x² + 8x + 27x + 18, then groups it as 4x(3x + 2) + ▢(3x + 2). What number goes in the box?

   9
6. 6.

   Bo splits 14x² + 47x + 30 into 14x² + 35x + 12x + 30 and groups it: 7x(2x + 5) + ▢(2x + 5). What number goes in the box?

   6
7. 7.

   Esme factors x³ − 2x² − 7x + 14 by grouping. Which answer is right?

   • (x − 2)(x² + 7)
   • x²(x − 2) − 7(x − 2)
   • (x − 2)(−7x²)
   • (x − 2)(x² − 7)
8. 8.

   Jun groups x³ − 6x² − 5x + 30 in two pairs. Which shows it as one product?

   • (x − 6)(x² + 5)
   • x²(x − 6) − 5(x − 6)
   • (x − 6)(x² − 5)
   • (x − 6)(−5x²)
9. 9.

   Kira draws x³ + 3x² − 8x − 24 as two rectangles with a shared side. Which is x³ + 3x² − 8x − 24 factored?

   • (x + 3)(x² + 8)
   • x²(x + 3) − 8(x + 3)
   • (x + 3)(x² − 8)
   • (x + 3)(−8x²)
10. 10.

    Luz checks four answers for x³ + 4x² − 6x − 24, factored by grouping. Which one is right?

    • x²(x + 4) − 6(x + 4)
    • (x + 4)(x² + 6)
    • (x + 4)(x² − 6)
    • (x + 4)(−6x²)