Factor completely: choose the method

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Kira factors 3x² − 27 as 3(x² − 9). Is it factored completely?

   • Yes: the GCF is out
   • No: it is 3(x − 3)(x + 3)
   • No: x can still come out of the bracket
   • No: it is 3(x − 3)²
2. 2.

   Luz writes 2x² − 98 as 2(x² − 49) and wants to stop there. Is it factored completely?

   • No: x can still come out of both terms
   • Yes: the GCF is out
   • No: it is 2(x − 7)²
   • No: it is 2(x − 7)(x + 7)
3. 3.

   Milo factors 4x² + 16 as 4(x² + 4) and puts the pencil down. Is it factored completely?

   • No: x can still come out of the second bracket
   • Yes: x² + 4 cannot be cut again
   • No: it is 4(x − 2)(x + 2)
   • No: it is 4(x + 2)²
4. 4.

   Noah checks a friend's work: 6x² + 150 = 6(x² + 25). Is it factored completely?

   • No: it is 6(x + 5)²
   • Yes: x² + 25 cannot be cut again
   • No: x can still come out
   • No: it is 6(x − 5)(x + 5)
5. 5.

   Ren takes out 2 first: 2x² − 6x − 20 = 2(x² − 3x − 10). Type them like 7, -1. What two numbers finish 2(x + ▢)(x + ▢)?

   -5, 2
6. 6.

   Tala takes out 4 first: 4x² − 36x + 80 = 4(x² − 9x + 20). Type them like 7, -1. What two numbers finish 4(x + ▢)(x + ▢)?

   -4, -5
7. 7.

   Zee takes out 5 first: 5x² + 10x − 40 = 5(x² + 2x − 8). Type them like 7, -1. What two numbers finish 5(x + ▢)(x + ▢)?

   4, -2
8. 8.

   Ari wants to factor 6x³ − 24x completely. Type powers like x^2. What greatest common factor comes out first?

   6x
9. 9.

   Bo starts to factor 4x³ + 28x² + 24x completely by taking out the GCF. Type powers like x^2. What is the GCF?

   4x
10. 10.

    Esme plans to factor 10x⁴ − 90x² all the way. Type powers like x^2. What GCF does Esme take out first?

    10x^2