Grade 11 · Math · Algebra 2

11th grade Factor sums and differences of cubes, and higher-degree polynomials worksheet

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Factor sums and differences of cubes, and higher-degree polynomials

Grade 11 Math Worksheet - Challenge Me

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

1.
On a worksheet, Luz factors 2x⁴ − 54x completely. Which answer is right?
- (x − 3)(x² + 3x + 9)
- 2x(x − 3)(x² + 3x + 9)
- 2x(x − 3)(x² − 3x + 9)
- 2x(x³ − 27)
2.
Noah factors 4x³ − 500 completely in pencil. Which answer is right?
- 4(x − 5)(x² + 5x + 25)
- 4(x − 5)(x² − 5x + 25)
- 4(x³ − 125)
- (x − 5)(x² + 5x + 25)
3.
On a puzzle card, Pia must factor x⁵ + 64x² completely. Which answer is right?
- x²(x³ + 64)
- (x + 4)(x² − 4x + 16)
- x²(x + 4)(x² + 4x + 16)
- x²(x + 4)(x² − 4x + 16)
In a notebook, Tala writes x³ − 64y³ as (x − 4y) times a quadratic. Type powers like y^2. What is the quadratic?
Zee factors 125x³ − 8y³ in pencil. One factor is 5x − 2y. What is the other factor?
On a puzzle card, 64x³ + y³ = (4x + y)( ? ). Esme needs the second factor. What is it?
7.
On a worksheet, Jun factors x⁴ + 2x³ − 8x − 16 completely by grouping. Which answer is right?
- (x + 2)(x − 2)(x² − 2x + 4)
- (x + 2)(x³ + 8)
- (x + 2)(x³ − 8)
- (x + 2)(x − 2)(x² + 2x + 4)
8.
In a notebook, Kira groups the four terms of x⁴ − 3x³ + 27x − 81 and keeps factoring. Which answer is fully factored?
- (x − 3)(x + 3)(x² + 3x + 9)
- (x − 3)(x³ + 27)
- (x − 3)(x³ − 27)
- (x − 3)(x + 3)(x² − 3x + 9)
9.
Luz factors x⁴ + x³ − 64x − 64 completely in pencil. Which answer is right?
- (x + 1)(x − 4)(x² − 4x + 16)
- (x + 1)(x³ − 64)
- (x + 1)(x³ + 64)
- (x + 1)(x − 4)(x² + 4x + 16)
10.
On a puzzle card, Milo must factor 2x⁴ − 5x³ + 16x − 40 completely. Which answer is right?
- (2x − 5)(x³ − 8)
- (2x − 5)(x + 2)(x² − 2x + 4)
- (2x − 5)(x³ + 8)
- (2x − 5)(x + 2)(x² + 2x + 4)

11th grade Factor sums and differences of cubes, and higher-degree polynomials worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Factor sums and differences of cubes, and higher-degree polynomials. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can factor a sum or a difference of cubes.
I can factor x⁴ − 13x² + 36 as a quadratic in x², then factor again.
I can group four terms and keep factoring until nothing factors.

Standard: A-SSE.A.2

Words to know

sum of cubes: Two cubes added: a³ + b³.

difference of cubes: One cube take away another: a³ − b³.

quadratic in x²: A polynomial like x⁴ − 5x² + 4, with x² in place of x.

factor completely: Keep factoring until no factor can be factored again.

Common mistakes

Your child used the same sign twice in the cube pattern, as in (a − b)(a² − ab + b²). Try: multiply the two factors back out and see which middle terms cancel.

Your child used the square pattern 2ab in a cube factor, where the middle term is ab. Try: multiply back and compare.

Your child doubled the number instead of squaring it for the last term.

What to say

Ask: what is 4 squared, and what is 4 doubled?

Questions parents ask

What is the most common mistake with factor sums and differences of cubes, and higher-degree polynomials?

Your child used the same sign twice in the cube pattern, as in (a − b)(a² − ab + b²). Try: multiply the two factors back out and see which middle terms cancel.

Are these 11th 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 2

See all Algebra 2

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