Grade 11 · Math · Algebra 2

11th grade Polynomial identities and the Binomial Theorem worksheet

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Polynomial identities and the Binomial Theorem

Grade 11 Math Worksheet - Challenge Me

NameDate

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

On a worksheet, Esme expands (2x + 1)³ with the cube pattern. Type powers like x^3. What is it in fewest terms?
In a notebook, Jun finds the volume of a cube with edge 3x − 1. Type powers like x^3. What is it in fewest terms?
Kira expands (2x − 3)³ in pencil. Type powers like x^3. What is it in fewest terms?
On a puzzle card, Luz builds (3x + 2)³ from 8 blocks. Type powers like x^3. What is it in fewest terms?
5.
In a notebook, Noah writes x² + 25 as a product of two binomials with i. Which one is right?
- (x + 5i)(x − 5i)
- (x + 5i)²
- (x + 25i)(x − 25i)
- (x + 5)(x − 5)
6.
Pia factors 4x² + 49 in pencil, using i. Which product equals 4x² + 49?
- (2x + 7)(2x − 7)
- (2x + 7i)²
- (2x + 49i)(2x − 49i)
- (2x + 7i)(2x − 7i)
7.
On a puzzle card, Ren needs 9x² + 16 as a product with i. Which one is right?
- (3x + 4)(3x − 4)
- (3x + 4i)²
- (3x + 16i)(3x − 16i)
- (3x + 4i)(3x − 4i)
In a notebook, Zee uses the Binomial Theorem on (x − 2)⁵. What is the coefficient of the x² term?
Esme expands (2x + 1)⁶ in pencil but only needs the x⁴ term. What is its coefficient?
On a puzzle card, Jun needs the x³ term of (2x − 3)⁴. What is its coefficient?

Polynomial identities and the Binomial Theorem. Every version has 10 questions, and the answer key prints on the second page.

Standard: A-APR.C.4, A-APR.C.5 (+), N-CN.C.8 (+)

identity: An equation true for every value of its letters.

Pascal's triangle: Rows of numbers; each is the sum of the two above it.

coefficient: The number in front of a term.

Binomial Theorem: Pascal's numbers give every term of (x + y)ⁿ.

Your child squared or cubed only the two ends and left out the middle parts, as in (a + b)² = a² + b². Try: draw the square and name all four pieces.

Your child counted the middle piece of a square once instead of twice. Try: draw the square and count the two matching strips.

Your child expanded a power of a difference with every sign plus. Try: write the second term with its minus sign and raise it to each power.

What is the most common mistake with polynomial identities and the binomial theorem?

Your child squared or cubed only the two ends and left out the middle parts, as in (a + b)² = a² + b². Try: draw the square and name all four pieces.

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.

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