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Grade 9 · Math · Algebra 1

9th grade Factor by grouping worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Factor by grouping

Grade 9 Math Worksheet - Building Confidence

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

  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?

  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?

  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?

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

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

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

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

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

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

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

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

    • (x + 1)(3x² + 4)
    • 3x²(x + 1) + 4(x + 1)
    • (x + 1)(x + 1)(3x² + 4)
    • (x + 1)(12x²)
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9th grade Factor by grouping worksheet – printable
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About this worksheet

Factor by grouping. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can split four terms into two pairs and take the GCF out of each pair.
  • I can take out the common bracket to write the polynomial as one product.
  • I can tell when the two brackets do not match, and reorder the terms to fix it.

Standard: A-SSE.A.2

Words to know

grouping: Putting four terms into two pairs and factoring each pair.

common bracket: The same bracket in both pairs, like (x + 4) in x²(x + 4) + 3(x + 4).

one product: Brackets multiplied, with no plus or minus left outside.

Common mistakes

Your child took out the common number of a pair but not the common letters.

Your child took out x where both terms share x².

Your child took out the common letters of a pair but not the common number.

What to say

Ask: does every term in the pair have x² in it?

Ask: what is the lower power of x in the pair?

Ask: which number divides both coefficients?

Questions parents ask

What is the most common mistake with factor by grouping?

Your child took out the common number of a pair but not the common letters.

How can I help my child with factor by grouping?

Ask: does every term in the pair have x² in it?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

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