Grade 9 · Math · Algebra 1

9th grade Factor completely: choose the method worksheet

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Factor completely: choose the method

Grade 9 Math Worksheet

NameDate

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

1.
Kira factors 4x³ − 36x for a puzzle card. Which answer is factored completely?
- 4x(x − 3)(x + 3)
- 4x(x² − 9)
- (2x − 6)(2x² + 6x)
- 4x(x − 3)²
2.
Luz and three friends each factor 3x³ + 18x² + 27x. Which answer is factored completely?
- 3(x³ + 6x² + 9x)
- (3x + 9)(x² + 3x)
- 3x(x + 3)²
- 3x(x² + 6x + 9)
3.
Milo wants 2x³ − 8x² − 42x factored all the way. Which answer is factored completely?
- 2x(x − 7)(x + 3)
- 2x(x² − 4x − 21)
- 2(x³ − 4x² − 21x)
- (2x − 14)(x² + 3x)
4.
Noah checks four answers for 5x⁴ − 20x². Which one is factored completely?
- 5x²(x − 2)²
- 5x²(x − 2)(x + 2)
- 5x(x³ − 4x)
- 5x²(x² − 4)
Tala factors 6x² − 150 completely as 6(x − ▢)(x + ▢). The same number goes in both boxes. What is that number?
Zee factors 4x² − 256 completely as 4(x − ▢)(x + ▢). The same number goes in both boxes. What is that number?
7.
Ari wants to factor 2x³ − 50x completely. Which step should come first?
- It cannot be factored
- Use the difference of squares right away
- Take out the GCF, 2x
- Take out 2 only
8.
Bo has 3x³ − 12x to factor completely. Which step comes first?
- Take out 3 only
- Use the difference of squares right away
- It cannot be factored
- Take out the GCF, 3x
9.
Esme wants to factor 4x² − 25 completely. Which step should come first?
- Use the difference of squares
- Take out the GCF, 2
- Find two numbers that multiply to −25 and add to 4
- It cannot be factored
10.
Jun gets 9x² − 64 on a puzzle card. Which step comes first to factor it completely?
- Use the difference of squares
- Take out the GCF, x
- Take out the GCF, 3
- It cannot be factored

9th grade Factor completely: choose the method worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Factor completely: choose the method. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can take out the greatest common factor first.
I can tell when a bracket can still be factored, and when it cannot (x² + 4).
I can factor a polynomial all the way, using more than one method.

Standard: A-SSE.A.2

Words to know

factor completely: Keep factoring until no bracket can be split with whole numbers.

greatest common factor (GCF): The biggest factor every term shares; it comes out first.

sum of squares: Like x² + 4: two squares added. It cannot be split.

Common mistakes

Your child took out the greatest common factor and stopped, though the part left could still be factored.

Your child wrote a difference of squares as a bracket squared, which brings back a middle term. Try: multiply the answer back out and compare.

Your child split a sum of two squares, like x² + 4, which cannot be factored with whole numbers.

What to say

Ask: can the bracket be factored again?

Ask: what is (x − 2)(x + 2) multiplied out?

Questions parents ask

What is the most common mistake with factor completely: choose the method?

Your child took out the greatest common factor and stopped, though the part left could still be factored.

How can I help my child with factor completely: choose the method?

Ask: can the bracket be factored again?

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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