Grade 11 · Math · Algebra 2

11th grade Divide polynomials by long division worksheet

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Divide polynomials by long division

Grade 11 Math Worksheet - Challenge Me

NameDate

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

Ari divides 4x³ + 4x² + 5x + 3 by 2x + 3 on a worksheet. Write the quotient, a comma, then the remainder. What are they?
Bo works out (4x³ + 4x² − 7x − 4) ÷ (2x − 1) in a notebook. Write the quotient, a comma, then the remainder. What are they?
Esme divides 4x³ + 2x² − 18x + 11 by 2x + 5 in pencil; the first step is 4x³ ÷ 2x = 2x². Write the quotient, a comma, then the remainder. What are they?
Jun works out (8x³ − 10x² − 9x + 14) ÷ (2x − 3) on a math club puzzle card. Write the quotient, a comma, then the remainder. What are they?
Kira divides x⁴ − 5x² + 2x − 5 by x + 2 on a worksheet. Write the quotient (powers like x^3), a comma, then the remainder. What are they?
Milo divides x⁴ − 6x² + x + 7 by x − 2 in pencil. Write the quotient, a comma, then the remainder. What are they?
Noah works out (2x⁴ − x³ + 4x − 3) ÷ (x − 3) from a math book. Write the quotient, a comma, then the remainder. What are they?
In a notebook, Ren divides a polynomial by x + 2. The quotient is 2x² − x + 3, remainder -5. What was the polynomial?
Tala divided a polynomial by x + 5 on a puzzle card and got x² − 4x, remainder 3. What was the polynomial?
Zee's division by x − 1, in pencil, gave the quotient 3x² + x − 2 and the remainder 6. What polynomial was divided?

11th grade Divide polynomials by long division worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Divide polynomials by long division. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can divide a polynomial by x + a or 2x + b with long division.
I can find the quotient and the remainder, and write quotient + remainder/divisor.
I can rebuild the polynomial from the divisor, quotient and remainder.

Standard: A-APR.D.6

Words to know

divisor: What you divide by: the side of the rectangle you know.

quotient: The answer to the division: the missing side.

remainder: The leftover piece that does not fit the rectangle.

placeholder 0: A 0 written for a missing power, like 0x², to keep the columns lined up.

Common mistakes

Your child added a product in long division where it must be subtracted. Try: multiply the answer back and compare with the start.

Your child wrote the next quotient term before subtracting the product.

Your child skipped a missing power instead of writing 0 for it, so the columns slid. Try: write every power from the highest down, with 0 where one is missing.

What to say

Ask: what is left after you take away the first product?

Questions parents ask

What is the most common mistake with divide polynomials by long division?

Your child added a product in long division where it must be subtracted. Try: multiply the answer back and compare with the start.

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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