Worksheets · Algebra 1

Solving quadratic equations by factoring worksheet for Algebra 1

Every equation here factors, because it was built from its own solutions. Many are not written in standard form yet, on every level, and moving everything to one side is the step students skip.

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

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Quadratics by Factoring

Date Period

Solve each equation by factoring.

  1. Solve by factoring

    4a2+32a−132=0
  2. 2p2+34p+109=−11
  3. b2+20b+116=16
  4. v2+2v−139=−19
  5. 2n2−8n−107=13
  6. 3b2−26b−131=−11
  7. 4m2−52m+120=0
  8. n2−n−117=15
  9. m2−121=0
  10. x2−21x+129=19

  1. Rewrite in standard form, then solve

    x(x−3)=10
  2. 3x2=26x−35
  3. x(x+10)=−24
  4. x(x+3)=18
  5. x(x−15)=−56
  6. x(x−2)=8
  7. x(x+7)=18
  8. x(x−9)=−20
  9. x(x+17)=−72
  10. x(x−4)=21

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Solving Quadratics by FactoringAnswer keyVersion 1

Date Period

Solve each equation by factoring.

  1. Solve by factoring

    4a2+32a−132=0{−11,3}
  2. 2p2+34p+109=−11{−12,−5}
  3. b2+20b+116=16{−10}
  4. v2+2v−139=−19{−12,10}
  5. 2n2−8n−107=13{−6,10}
  6. 3b2−26b−131=−11{−103,12}
  7. 4m2−52m+120=0{3,10}
  8. n2−n−117=15{−11,12}
  9. m2−121=0{−11,11}
  10. x2−21x+129=19{10,11}

  1. Rewrite in standard form, then solve

    x(x−3)=10{−2,5}
  2. 3x2=26x−35{53,7}
  3. x(x+10)=−24{−6,−4}
  4. x(x+3)=18{−6,3}
  5. x(x−15)=−56{7,8}
  6. x(x−2)=8{−2,4}
  7. x(x+7)=18{−9,2}
  8. x(x−9)=−20{4,5}
  9. x(x+17)=−72{−9,−8}
  10. x(x−4)=21{−3,7}

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

x2−11x+19=−5

  1. Get everything on one side first: add 5 to both sides.
  2. That gives x² - 11x + 24 = 0.
  3. Factor: (x - 3)(x - 8) = 0, so either parenthesis can be zero.

The answer is {3,8}.

Where students go wrong

Factoring before moving everything to one side. The zero product rule only works against zero: from (x - 3)(x - 8) = -5 you can say nothing at all, because two numbers multiplying to -5 could be anything.

Also called the zero product property or solving quadratics by factoring.

What you can put on this worksheet

Factor, then set each factor to zero
v2−2v−35=0 → {−5,7}
Already factored, or a common factor only
4v2+24v=0 → {−6,0}
Rearrange to standard form first
x(x−2)=35 → {−5,7}
Squares on both sides
4k2−9k+4=3k2−4k → {1,4}
Two fraction answers
20x2+19x+9=6 → {−34,−15}

Questions about these worksheets

Yes. Every solving quadratic equations by factoring 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 solving quadratic equations by factoring 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 5: factor, then set each factor to zero, already factored, or a common factor only, rearrange to standard form first, squares on both sides and two fraction answers. Tick as many as you want and set how many of each, or let it spread them evenly.

Factoring before moving everything to one side. The zero product rule only works against zero: from (x - 3)(x - 8) = -5 you can say nothing at all, because two numbers multiplying to -5 could be anything.