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Worksheets›Algebra 1›Polynomials & factoring›Dividing polynomials by monomials

Dividing Polynomials by Monomials Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 1CCSS HSA.APR.D.6Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Dividing by a number

  1. 1.42x2 + 48x − 66
  2. 2.24x2 + 4x − 44
  3. 3.8x2 + 364
  4. 4.−5x2 − 30x − 455
  5. 5.8x2 + 36x − 244
  6. 6.20x2 − 8x − 324
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Split the fraction into one fraction per term, then divide each: divide the numbers and subtract the powers of x.

Easy10x2 − 2x + 42Dividing by a numberMedium16x3 − 8x2 − 4x4xDividing by a positive monomialHard10x4 − 10x3 + 35x2−5x2Dividing by a negative monomial

How to solve it: a worked example

Divide. Write each answer in standard form.

  1. Start−6x2 − 42x + 246
  2. Divide each term by the monomial−6x26 + −42x6 + 246
  3. Then−x2 − 7x + 4
  4. Answer−x2 − 7x + 4

Common mistakes to watch for

  • Dividing only the first term.
  • Dividing the exponents instead of subtracting them: x⁶ ÷ x² is x⁴.
  • Losing track of signs when the divisor is negative.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Adding and subtracting polynomialsMultiplying polynomialsFactoring trinomialsFactoring: GCF and special productsMulti-step inequalities

FAQ

Do you divide every term?

Yes. (12x³ − 8x² + 4x) ÷ 4x = 3x² − 2x + 1. Forgetting to divide the last term is a common slip.

What happens to a term like 4x ÷ 4x?

It equals 1, not 0, because anything nonzero divided by itself is 1. The exponents subtract to x⁰ = 1.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix dividing polynomials by monomials with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.