(6x^4 + 21x^3 + 8x^2 - 11x + 13) divided by (2x + 3)

3x^3 + 6x^2 - 5x + 2 + (7)/(2x + 3)

(-2x^5 - 9x^4 - 6x^3 + 10x^2 + 4x + 7) divided by (x^2 + 3x + 1)

-2x^3 - 3x^2 + 5x - 2 + (5x + 9)/(x^2 + 3x + 1)

Dividing polynomials worksheet for Algebra 1

Three kinds of question, so the student has to look at the divisor and choose the method. Dividing by a single term splits into one division per term. Dividing by x minus a number can be done by long division or by the synthetic table. Dividing by 2x + 3, or by a quadratic, cannot be done synthetically and has to be long division. Easy divides exactly; the harder levels leave a remainder to write as a fraction.

Also taught in Precalculus and Algebra 2, each at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Dividing Polynomials Date Period Divide. Divide by a monomial $\frac{30 x^{3} + 10 x^{2} + 25 x}{5 x}$ $\frac{18 x^{3} - 18 x^{2} + 9 x}{3 x}$ $\frac{4 x^{4} - 4 x^{3} + 4 x^{2}}{2 x^{2}}$ $\frac{- 5 x^{3} + 10 x^{2} + 20 x}{5 x}$ $\frac{- 4 x^{4} - 20 x^{3} - 16 x^{2}}{4 x^{2}}$ Divide by $x - c$ $\frac{- 5 p^{3} + 38 p^{2} + 14 p + 6}{p - 8}$ $\frac{5 m^{3} - 38 m^{2} - 57 m - 66}{m - 9}$ $\frac{6 y^{3} + 47 y^{2} - 62 y}{y + 9}$ $\frac{- 5 p^{3} + 47 p^{2} - 61 p + 51}{p - 8}$ $\frac{5 m^{3} - 34 m^{2} - 15 m + 45}{m - 7}$ Divide by $ax + b$ or a quadratic $\frac{- 18 r^{3} + 45 r^{2} - 16 r - 19}{3 r - 4}$ $\frac{- 21 b^{3} - 7 b^{2} + 34 b + 4}{3 b + 4}$ $\frac{- 9 n^{3} + 19 n + 7}{3 n + 2}$ $\frac{10 x^{3} + 23 x^{2} + 14 x + 2}{2 x + 3}$ $\frac{- 4 v^{3} + 18 v^{2} - 34 v + 38}{2 v - 5}$ Divide with a missing term $(x^{3} + x^{2} - 7) \div (x + 1)$ $(x^{3} + 3 x - 3) \div (x + 2)$ $(x^{3} - 8 x^{2} - 6) \div (x - 4)$ $(x^{3} + 3 x^{2} + 4) \div (x - 1)$ $(x^{3} - 8 x^{2} + 2) \div (x + 3)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Dividing Polynomials

Date Period

Divide.

Divide by a monomial
$\frac{30 x^{3} + 10 x^{2} + 25 x}{5 x}$
$\frac{18 x^{3} - 18 x^{2} + 9 x}{3 x}$
$\frac{4 x^{4} - 4 x^{3} + 4 x^{2}}{2 x^{2}}$
$\frac{- 5 x^{3} + 10 x^{2} + 20 x}{5 x}$
$\frac{- 4 x^{4} - 20 x^{3} - 16 x^{2}}{4 x^{2}}$

Divide by $x - c$
$\frac{- 5 p^{3} + 38 p^{2} + 14 p + 6}{p - 8}$
$\frac{5 m^{3} - 38 m^{2} - 57 m - 66}{m - 9}$
$\frac{6 y^{3} + 47 y^{2} - 62 y}{y + 9}$
$\frac{- 5 p^{3} + 47 p^{2} - 61 p + 51}{p - 8}$
$\frac{5 m^{3} - 34 m^{2} - 15 m + 45}{m - 7}$

Divide by $ax + b$ or a quadratic
$\frac{- 18 r^{3} + 45 r^{2} - 16 r - 19}{3 r - 4}$
$\frac{- 21 b^{3} - 7 b^{2} + 34 b + 4}{3 b + 4}$
$\frac{- 9 n^{3} + 19 n + 7}{3 n + 2}$
$\frac{10 x^{3} + 23 x^{2} + 14 x + 2}{2 x + 3}$
$\frac{- 4 v^{3} + 18 v^{2} - 34 v + 38}{2 v - 5}$

Divide with a missing term
$(x^{3} + x^{2} - 7) \div (x + 1)$
$(x^{3} + 3 x - 3) \div (x + 2)$
$(x^{3} - 8 x^{2} - 6) \div (x - 4)$
$(x^{3} + 3 x^{2} + 4) \div (x - 1)$
$(x^{3} - 8 x^{2} + 2) \div (x + 3)$



Sigma Prep · sigmaprep.io/worksheets Name Dividing PolynomialsAnswer keyVersion 1 Date Period Divide. Divide by a monomial $\frac{30 x^{3} + 10 x^{2} + 25 x}{5 x}$ $6 x^{2} + 2 x + 5$ $\frac{18 x^{3} - 18 x^{2} + 9 x}{3 x}$ $6 x^{2} - 6 x + 3$ $\frac{4 x^{4} - 4 x^{3} + 4 x^{2}}{2 x^{2}}$ $2 x^{2} - 2 x + 2$ $\frac{- 5 x^{3} + 10 x^{2} + 20 x}{5 x}$ $- x^{2} + 2 x + 4$ $\frac{- 4 x^{4} - 20 x^{3} - 16 x^{2}}{4 x^{2}}$ $- x^{2} - 5 x - 4$ Divide by $x - c$ $\frac{- 5 p^{3} + 38 p^{2} + 14 p + 6}{p - 8}$ $- 5 p^{2} - 2 p - 2 - \frac{10}{p - 8}$ $\frac{5 m^{3} - 38 m^{2} - 57 m - 66}{m - 9}$ $5 m^{2} + 7 m + 6 - \frac{12}{m - 9}$ $\frac{6 y^{3} + 47 y^{2} - 62 y}{y + 9}$ $6 y^{2} - 7 y + 1 - \frac{9}{y + 9}$ $\frac{- 5 p^{3} + 47 p^{2} - 61 p + 51}{p - 8}$ $- 5 p^{2} + 7 p - 5 + \frac{11}{p - 8}$ $\frac{5 m^{3} - 34 m^{2} - 15 m + 45}{m - 7}$ $5 m^{2} + m - 8 - \frac{11}{m - 7}$ Divide by $ax + b$ or a quadratic $\frac{- 18 r^{3} + 45 r^{2} - 16 r - 19}{3 r - 4}$ $- 6 r^{2} + 7 r + 4 - \frac{3}{3 r - 4}$ $\frac{- 21 b^{3} - 7 b^{2} + 34 b + 4}{3 b + 4}$ $- 7 b^{2} + 7 b + 2 - \frac{4}{3 b + 4}$ $\frac{- 9 n^{3} + 19 n + 7}{3 n + 2}$ $- 3 n^{2} + 2 n + 5 - \frac{3}{3 n + 2}$ $\frac{10 x^{3} + 23 x^{2} + 14 x + 2}{2 x + 3}$ $5 x^{2} + 4 x + 1 - \frac{1}{2 x + 3}$ $\frac{- 4 v^{3} + 18 v^{2} - 34 v + 38}{2 v - 5}$ $- 2 v^{2} + 4 v - 7 + \frac{3}{2 v - 5}$ Divide with a missing term $(x^{3} + x^{2} - 7) \div (x + 1)$ $x^{2} - \frac{7}{x + 1}$ $(x^{3} + 3 x - 3) \div (x + 2)$ $x^{2} - 2 x + 7 - \frac{17}{x + 2}$ $(x^{3} - 8 x^{2} - 6) \div (x - 4)$ $x^{2} - 4 x - 16 - \frac{70}{x - 4}$ $(x^{3} + 3 x^{2} + 4) \div (x - 1)$ $x^{2} + 4 x + 4 + \frac{8}{x - 1}$ $(x^{3} - 8 x^{2} + 2) \div (x + 3)$ $x^{2} - 11 x + 33 - \frac{97}{x + 3}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Dividing PolynomialsAnswer keyVersion 1

Date Period

Divide.

Divide by a monomial
$\frac{30 x^{3} + 10 x^{2} + 25 x}{5 x}$ $6 x^{2} + 2 x + 5$
$\frac{18 x^{3} - 18 x^{2} + 9 x}{3 x}$ $6 x^{2} - 6 x + 3$
$\frac{4 x^{4} - 4 x^{3} + 4 x^{2}}{2 x^{2}}$ $2 x^{2} - 2 x + 2$
$\frac{- 5 x^{3} + 10 x^{2} + 20 x}{5 x}$ $- x^{2} + 2 x + 4$
$\frac{- 4 x^{4} - 20 x^{3} - 16 x^{2}}{4 x^{2}}$ $- x^{2} - 5 x - 4$

Divide by $x - c$
$\frac{- 5 p^{3} + 38 p^{2} + 14 p + 6}{p - 8}$ $- 5 p^{2} - 2 p - 2 - \frac{10}{p - 8}$
$\frac{5 m^{3} - 38 m^{2} - 57 m - 66}{m - 9}$ $5 m^{2} + 7 m + 6 - \frac{12}{m - 9}$
$\frac{6 y^{3} + 47 y^{2} - 62 y}{y + 9}$ $6 y^{2} - 7 y + 1 - \frac{9}{y + 9}$
$\frac{- 5 p^{3} + 47 p^{2} - 61 p + 51}{p - 8}$ $- 5 p^{2} + 7 p - 5 + \frac{11}{p - 8}$
$\frac{5 m^{3} - 34 m^{2} - 15 m + 45}{m - 7}$ $5 m^{2} + m - 8 - \frac{11}{m - 7}$

Divide by $ax + b$ or a quadratic
$\frac{- 18 r^{3} + 45 r^{2} - 16 r - 19}{3 r - 4}$ $- 6 r^{2} + 7 r + 4 - \frac{3}{3 r - 4}$
$\frac{- 21 b^{3} - 7 b^{2} + 34 b + 4}{3 b + 4}$ $- 7 b^{2} + 7 b + 2 - \frac{4}{3 b + 4}$
$\frac{- 9 n^{3} + 19 n + 7}{3 n + 2}$ $- 3 n^{2} + 2 n + 5 - \frac{3}{3 n + 2}$
$\frac{10 x^{3} + 23 x^{2} + 14 x + 2}{2 x + 3}$ $5 x^{2} + 4 x + 1 - \frac{1}{2 x + 3}$
$\frac{- 4 v^{3} + 18 v^{2} - 34 v + 38}{2 v - 5}$ $- 2 v^{2} + 4 v - 7 + \frac{3}{2 v - 5}$

Divide with a missing term
$(x^{3} + x^{2} - 7) \div (x + 1)$ $x^{2} - \frac{7}{x + 1}$
$(x^{3} + 3 x - 3) \div (x + 2)$ $x^{2} - 2 x + 7 - \frac{17}{x + 2}$
$(x^{3} - 8 x^{2} - 6) \div (x - 4)$ $x^{2} - 4 x - 16 - \frac{70}{x - 4}$
$(x^{3} + 3 x^{2} + 4) \div (x - 1)$ $x^{2} + 4 x + 4 + \frac{8}{x - 1}$
$(x^{3} - 8 x^{2} + 2) \div (x + 3)$ $x^{2} - 11 x + 33 - \frac{97}{x + 3}$

How to do these

$\frac{x^{3} + 2 x^{2} - 5 x + 6}{x + 3}$

x³ divided by x is x², so that is the first term.
Multiply back and subtract, then bring down.
Carry on until the degree drops below the divisor.

The answer is $x^{2} - x - 2 + \frac{12}{x + 3}$ .

Where students go wrong

Forgetting a missing term. If there is no x² term you still need a placeholder, because the columns have to line up. Writing the dividend with every power present, using zero where needed, prevents most of the damage.

Also called polynomial long division.

What you can put on this worksheet

Divide by a monomial: $\frac{4 x^{4} - 16 x^{3}}{4 x^{2}}$ → $x^{2} - 4 x$
Divide by x - c: long or synthetic division: $\frac{2 v^{3} - 8 v^{2} - 13 v + 15}{v - 5}$ → $2 v^{2} + 2 v - 3$
Divide by ax + b or a quadratic: long division only: $\frac{- 10 v^{3} - 35 v^{2} - 31 v - 15}{2 v + 5}$ → $- 5 v^{2} - 5 v - 3$
A missing term: $(x^{3} - 8) \div (x - 2)$ → $x^{2} + 2 x + 4$
Remainders, ax + b, a missing term, terms out of order: $\frac{15 r^{2} + 23 r - 23}{5 r + 1}$ → $3 r + 4 - \frac{27}{5 r + 1}$
By ax + b with a not 1: $(6 x^{4} + 21 x^{3} + 8 x^{2} - 11 x + 13) \div (2 x + 3)$ → $3 x^{3} + 6 x^{2} - 5 x + 2 + \frac{7}{2 x + 3}$
By a quadratic trinomial or a cubic: $(- 2 x^{5} - 9 x^{4} - 6 x^{3} + 10 x^{2} + 4 x + 7) \div (x^{2} + 3 x + 1)$ → $- 2 x^{3} - 3 x^{2} + 5 x - 2 + \frac{5 x + 9}{x^{2} + 3 x + 1}$

Questions about these worksheets

Yes. Every dividing polynomials sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the dividing polynomials questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 7: divide by a monomial, divide by x - c: long or synthetic division, divide by ax + b or a quadratic: long division only, a missing term, remainders, ax + b, a missing term, terms out of order, by ax + b with a not 1 and by a quadratic trinomial or a cubic. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing polynomials worksheet for Algebra 1

Select your difficulty

Divide by a monomial

Divide by x−cx - cx−c

Divide by ax+bax + bax+b or a quadratic

Divide with a missing term

Divide by a monomial

Divide by x−cx - cx−c

Divide by ax+bax + bax+b or a quadratic

Divide with a missing term

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these dividing polynomials worksheets free?+

Do the dividing polynomials worksheets come with an answer key?+

Are these dividing polynomials worksheets printable?+

What grade are these dividing polynomials worksheets for?+

Can I get a different version of the same dividing polynomials worksheet?+

Is this a free alternative to Kuta Software for dividing polynomials?+

Can I choose how hard the dividing polynomials questions are?+

What kinds of question are on a dividing polynomials worksheet?+

What do students get wrong with dividing polynomials?+

Divide by $x - c$

Divide by $ax + b$ or a quadratic

Divide by $x - c$

Divide by $ax + b$ or a quadratic