Grade 11 · Math · Algebra 2

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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

Grade 11 Math Worksheet - Building Confidence

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

On a worksheet, Zee factors x³ + 27 = (x + 3)(x² + ▢x + ▢). Write the two numbers with a comma, signs included. What are they?
In a notebook, Esme writes 27x³ − 64 = (3x − 4)(9x² + ▢x + ▢). Write the two box numbers with a comma. What are they?
On a puzzle card, 8x³ − 125 = (2x − 5)(4x² + ▢x + ▢). Kira fills the boxes. Type both numbers with a comma. What are they?
On a worksheet, Luz factors x⁴ − 16x² − 225 = (x² + ▢)(x² − ▢). Write the two numbers, first box first, with a comma. What are they?
In a notebook, Milo treats x⁴ + 27x² − 324 as a quadratic in x²: (x² + ▢)(x² − ▢). Type both numbers with a comma. What are they?
On a puzzle card, x⁴ − 11x² − 900 = (x² + ▢)(x² − ▢). Pia fills the boxes. Type both numbers with a comma. What are they?
On a worksheet, Ren groups x³ + 3x² + 4x + 12 as x²(x + 3) + 4(x + 3). Type powers like x^2. What is the factor besides x + 3?
In a notebook, Tala writes x³ − 2x² − 5x + 10 = x²(x − 2) − 5(x − 2). What is the other factor, besides x − 2?
Zee factors 2x³ + 5x² + 6x + 15 in pencil as x²(2x + 5) + 3(2x + 5). What is the factor that goes with 2x + 5?
On a puzzle card, x³ + 4x² − 7x − 28 = x²(x + 4) − 7(x + 4). Esme takes out x + 4. What is the other factor?

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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