Factor x^2 + bx + c

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Jun draws x² + 9x + 20 as a rectangle. Its two side numbers multiply to 20 and add to 9. Type them like 1, -9. What are the two numbers?

   4, 5
2. 2.

   Kira lays tiles for x² + 13x + 30 in a rectangle. The side numbers multiply to 30 and add to 13. Type them like 1, -9. What are they?

   3, 10
3. 3.

   Luz sketches x² + 12x + 32 as a quilt block. The side numbers multiply to 32 and add to 12. Type them like 1, -9. What are they?

   4, 8
4. 4.

   Milo cuts x² + 14x + 45 into four pieces of paper. The side numbers multiply to 45 and add to 14. Type them like 1, -9. What are they?

   5, 9
5. 5.

   Pia is very sure that x² + 10x + 16 = (x + 4)(x + 4). Is Pia right?

   • No. The numbers must add to 16.
   • No. It multiplies back to x² + 8x + 16.
   • Yes. 4 × 4 = 16.
   • Yes. Both brackets start with x, so the factoring works.
6. 6.

   Ren writes x² + 11x + 30 = (x + 5)(x + 6) on the board. Is Ren right?

   • Yes. It multiplies back to x² + 11x + 30.
   • No. The two numbers must be the same.
   • No. The numbers must add to 30.
   • No. It multiplies back to x² + 30x + 11.
7. 7.

   Tala checks a friend's answer: x² + 15x + 54 = (x + 3)(x + 18). Is the friend right?

   • Yes. 3 × 18 = 54.
   • Yes. Both brackets start with x, so the friend is right.
   • No. The numbers must add to 54.
   • No. It multiplies back to x² + 21x + 54.
8. 8.

   Ari is making a rug plan for x² + 10x + 21. Which is x² + 10x + 21 factored?

   • (x + 3)(x + 7)
   • (x − 3)(x − 7)
   • (x + 2)(x + 8)
   • (x + 1)(x + 21)
9. 9.

   Bo builds x² + 16x + 28 from tiles. Which pair of sides fits?

   • (x − 2)(x − 14)
   • (x + 6)(x + 10)
   • (x + 4)(x + 7)
   • (x + 2)(x + 14)
10. 10.

    Esme needs the sides of a tabletop of x² + 17x + 42 square units. Which is x² + 17x + 42 factored?

    • (x + 6)(x + 7)
    • (x + 8)(x + 9)
    • (x − 3)(x − 14)
    • (x + 3)(x + 14)