Grade 9 · Math · Algebra 1

9th grade Factor by grouping worksheet

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Factor by grouping

Grade 9 Math Worksheet - Challenge Me

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

1.
Milo groups xy + 3x + 2y + 6, which has two letters. Which is it factored?
- (x + 2)(y + 3)
- x(y + 3) + 2(y + 3)
- (x + 3)(y + 2)
- (y + 3)(2x)
2.
Noah pairs the terms of xy − 4x + 5y − 20 to find a shared bracket. Which is it factored?
- x(y − 4) + 5(y − 4)
- (y − 4)(5x)
- (x + 5)(y − 4)
- (x − 4)(y + 5)
3.
Ren checks four answers for 2xy + 10x + 3y + 15. Which one is it factored?
- 2x(y + 5) + 3(y + 5)
- (2x + 3)(y + 5)
- (y + 5)(6x)
- (2x + 5)(y + 3)
Tala sees that 3x³ − 8 + 12x² − 2x will not group in this order. Reordered and grouped, it is (x + ▢)(3x² − 2). What number goes in the box?
Zee has to move the terms of 2x³ − 15 + 10x² − 3x before grouping. Grouped, it is (x + ▢)(2x² − 3). What number goes in the box?
Ari reorders 5x³ − 12 + 30x² − 2x so pairs share a factor. Factored, it is (x + ▢)(5x² − 2). What number goes in the box?
Bo rearranges 2x³ − 35 + 14x² − 5x and groups it as (x + ▢)(2x² − 5). What number goes in the box?
8.
Esme groups x³ + 3x² + 4x + 6 as x²(x + 3) + 2(2x + 3). What does this grouping show?
- The brackets differ, so this grouping does not factor it.
- It factors as (2x + 3)(x² + 2).
- It is already factored, since each pair has been factored on its own.
- It factors as (x + 3)(x² + 2).
9.
Jun tries grouping x³ + 5x² + 3x + 9 and gets x²(x + 5) + 3(x + 3). What does this show?
- It is already factored, because each pair has its own common factor.
- It factors as (x + 5)(x² + 3).
- It factors as (x + 3)(x² + 3).
- The brackets differ, so this grouping does not factor it.
10.
Luz writes x³ − 2x² + 5x − 15 = x²(x − 2) + 5(x − 3). What does this grouping show?
- It factors as (x − 3)(x² + 5).
- The brackets differ, so this grouping does not factor it.
- It is already factored.
- It factors as (x − 2)(x² + 5).

9th grade Factor by grouping worksheet – printable — Print: 1 2 3 4 5 6

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

See all Algebra 1

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