Factor x^2 + bx + c

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   For x² − 3x − 28, Jun needs two side numbers that multiply to −28 and add to −3. Type them like 1, -9. What are they?

   -7, 4
2. 2.

   Kira wants the sides of x² + 4x − 45. The side numbers multiply to −45 and add to 4. Type them like 1, -9. What are they?

   9, -5
3. 3.

   Milo has a puzzle card for x² + x − 42: two numbers with product −42 and sum 1. Type them like 1, -9. What are they?

   7, -6
4. 4.

   Noah wants to factor x² + 2x − 35. Which answer is right?

   • (x + 7)(x − 5)
   • (x − 7)(x + 5)
   • (x + 35)(x − 1)
   • (x + 7)(x + 5)
5. 5.

   Pia and a friend disagree about x² − 4x − 32. Which is x² − 4x − 32 factored?

   • (x − 8)(x + 4)
   • (x + 8)(x + 4)
   • (x + 8)(x − 4)
   • (x − 16)(x + 2)
6. 6.

   Ren checks four answers for x² − x − 56. Which one is right?

   • (x + 8)(x − 7)
   • (x + 8)(x + 7)
   • (x − 14)(x + 4)
   • (x − 8)(x + 7)
7. 7.

   Tala needs the sides of x² + 6x − 27 for a puzzle. Which is x² + 6x − 27 factored?

   • (x + 9)(x − 3)
   • (x − 9)(x + 3)
   • (x + 9)(x + 3)
   • (x + 27)(x − 1)
8. 8.

   Ari has one side of x² + 3x − 40: x² + 3x − 40 = (x − 5)(x + ▢). It may be negative. What number goes in the box?

   8
9. 9.

   Bo has one side of x² − 12x + 27: x² − 12x + 27 = (x − 3)(x + ▢). It may be negative. What number goes in the box?

   -9
10. 10.

    Esme has one side of x² + 5x − 36: x² + 5x − 36 = (x + 9)(x + ▢). It may be negative. What number goes in the box?

    -4