Polynomials
Multiplying binomials worksheets
Expand ten products of two binomials. Choose among four expression structures, form every term pair and collect like terms with a separate worked key.
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Dividing polynomials worksheets
Divide polynomials by monic linear divisors in ten expression problems or six long-division problems. Choose binomial, trinomial, four-term or mixed dividends and check exact quotient-and-remainder keys.
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Divide each polynomial by the monic linear divisor. Write the quotient and any remainder over the original divisor.
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Customize this worksheetConnect quotient, divisor and remainder
Expression mode gives ten compact division questions. Long-division mode gives six bracket-form questions with room to calculate. Both use the same exact polynomial pool, so the first six problems stay unchanged when only the presentation changes.
Check each result by multiplying the divisor by the quotient and adding the signed remainder. The divisor must be nonzero wherever the remainder fraction is used.
Learning objective
What this activity builds
Find an exact polynomial quotient and signed scalar remainder, then verify the division identity.
Worked example
Divide 2x² − 11x − 18 by x − 7.
2x + 3 + 3/(x − 7).
The quotient is 2x + 3 and the remainder is 3. Check that (x − 7)(2x + 3) + 3 equals the original dividend.
Teaching notes
Make the practice count
- Keep descending powers aligned, including a zero placeholder for a missing power when it helps.
- Use the divisor constant with its sign during synthetic division.
- Write a negative remainder with subtraction, not as addition of a negative fraction.
- Verify that divisor times quotient plus remainder reconstructs the dividend.
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Choose your options, update the preview, then download the exact same pages.
Choose the expression structures to practice. Answer editions show the steps for each problem.
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Polynomials
Factoring quadratic polynomials worksheets
Factor ten quadratic binomials and trinomials completely over the integers. Choose factorable-only practice or include two prime quadratics, and vary monic and nonmonic leading coefficients.
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