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 - Challenge Me

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

1.
Kira factors x⁴ − 16 with two cuts in a row. Which answer is factored completely?
- (x − 2)(x + 2)(x − 2)(x + 2)
- (x² + 4)(x² − 4)
- (x² + 4)(x − 2)(x + 2)
- It cannot be factored
2.
Luz wants 16x⁴ − 1 factored all the way. Which answer is factored completely?
- (2x − 1)(2x + 1)(2x − 1)(2x + 1)
- It cannot be factored
- (4x² + 1)(4x² − 1)
- (4x² + 1)(2x − 1)(2x + 1)
3.
Milo takes out the GCF of 2x⁴ − 162 and keeps going. Which answer is factored completely?
- 2(x − 3)(x + 3)(x − 3)(x + 3)
- 2(x⁴ − 81)
- 2(x² + 9)(x − 3)(x + 3)
- 2(x² + 9)(x² − 9)
4.
Noah factors 3x⁴ − 48 for a challenge card. Which answer is factored completely?
- 3(x² + 4)(x − 2)(x + 2)
- 3(x² + 4)(x² − 4)
- 3(x⁴ − 16)
- 3(x − 2)(x + 2)(x − 2)(x + 2)
5.
Ren factors x³ − 5x² − 4x + 20 by grouping, then looks again. Which answer is factored completely?
- (x − 5)(x² + 4)
- (x − 5)(x − 2)²
- (x − 5)(x − 2)(x + 2)
- (x − 5)(x² − 4)
6.
Tala wants 2x³ + 3x² − 8x − 12 factored all the way. Which answer is factored completely?
- (2x + 3)(x² + 4)
- (2x + 3)(x² − 4)
- (2x + 3)(x − 2)(x + 2)
- (2x + 3)(x − 2)²
7.
Zee checks four answers for x³ + 4x² − 25x − 100. Which one is factored completely?
- (x + 4)(x² − 25)
- (x + 4)(x² + 25)
- (x + 4)(x − 5)²
- (x + 4)(x − 5)(x + 5)
Bo factors 6x² − 9x − 60 completely and gets 3(2x + 5)(x + ▢). It may be negative. What number goes in the box?
Esme factors 10x² + 22x − 24 completely and gets 2(5x − 4)(x + ▢). It may be negative. What number goes in the box?
Jun factors 10x² − 46x + 24 completely and gets 2(5x − 3)(x + ▢). It may be negative. What number goes in the box?

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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