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

NameDate

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

On a worksheet, Jun factors 8x³ − 27 = (2x − 3)( ? ). Type powers like x^2. What is the second factor?
In a notebook, Kira writes 27x³ + 8 as (3x + 2) times a quadratic. What is the quadratic?
On a puzzle card, 125x³ + 8 = (5x + 2)( ? ). Milo needs the second factor. What is it?
4.
On a worksheet, Noah factors x³ − 5x² − 9x + 45 completely by grouping. Which answer is right?
- (x − 5)(x² − 9)
- (x − 5)(x − 3)(x + 3)
- (x − 5)(x² + 9)
- (x + 5)(x − 3)(x + 3)
5.
In a notebook, Pia groups the four terms of x³ + 2x² − 16x − 32 and factors completely. Which answer is right?
- (x + 2)(x² + 16)
- (x − 2)(x − 4)(x + 4)
- (x + 2)(x² − 16)
- (x + 2)(x − 4)(x + 4)
6.
Ren factors 2x³ − x² − 50x + 25 completely in pencil. Which answer is right?
- (2x − 1)(x² − 25)
- (2x − 1)(x − 5)(x + 5)
- (2x + 1)(x − 5)(x + 5)
- (2x − 1)(x² + 25)
7.
On a puzzle card, Tala must factor x³ + 7x² − 4x − 28 completely. Which answer is right?
- (x + 7)(x² − 4)
- (x − 7)(x − 2)(x + 2)
- (x + 7)(x − 2)(x + 2)
- (x + 7)(x² + 4)
8.
On a worksheet, Zee factors x⁴ − 13x² + 36 completely. Which answer is right?
- (x − 2)(x + 2)(x − 3)(x + 3)
- (x² − 4)(x² − 9)
- (x − 4)(x − 9)
- (x² − 2)(x² − 3)
9.
In a notebook, Esme treats x⁴ − 10x² + 9 as a quadratic in x² and factors completely. Which answer is right?
- (x − 1)(x + 1)(x − 3)(x + 3)
- (x − 1)(x − 9)
- (x² − 1)(x² − 9)
- (x² − 1)(x² − 3)
10.
Jun factors x⁴ − 5x² − 36 completely in pencil. Which answer is right?
- (x − 9)(x + 4)
- (x − 3)(x + 3)(x² + 4)
- (x² − 3)(x² + 2)
- (x² − 9)(x² + 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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