Worksheets · Algebra 1

Factoring trinomials (a = 1) worksheet

Every question here has a leading coefficient of 1. Pick the types you want, choose how many questions, and print. Every sheet is generated fresh, so you can print a different one for each class period, and the answer key is built from the factors so it is always right.

Select your difficulty

Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Factoring Trinomials (a = 1)

Date Period

Factor each completely.

  1. v2+20v+99
  2. a222a+120
  3. p2+2p120
  4. 4b2+76b+360
  5. 2r238r+180
  6. v2+v90
  7. a2+19a+90
  8. r221r+108
  9. 3r29r324
  10. n2+19n+90
  11. 5b2100b+495
  12. y23y108
  13. a2+20a+100
  14. y223y+132
  15. x23x108
  16. v2+22v+120
  17. a220a+99
  18. n2+3n108
  19. m2+19m+90
  20. x222x+121

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

Sigma Prep · sigmaprep.io/worksheets

Name

Factoring Trinomials (a = 1)Answer keyVersion 1

Date Period

Factor each completely.

  1. v2+20v+99(v+9)(v+11)
  2. a222a+120(a12)(a10)
  3. p2+2p120(p10)(p+12)
  4. 4b2+76b+3604(b+9)(b+10)
  5. 2r238r+1802(r10)(r9)
  6. v2+v90(v9)(v+10)
  7. a2+19a+90(a+9)(a+10)
  8. r221r+108(r12)(r9)
  9. 3r29r3243(r12)(r+9)
  10. n2+19n+90(n+9)(n+10)
  11. 5b2100b+4955(b11)(b9)
  12. y23y108(y12)(y+9)
  13. a2+20a+100(a+10)2
  14. y223y+132(y12)(y11)
  15. x23x108(x12)(x+9)
  16. v2+22v+120(v+10)(v+12)
  17. a220a+99(a11)(a9)
  18. n2+3n108(n9)(n+12)
  19. m2+19m+90(m+9)(m+10)
  20. x222x+121(x11)2

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

How to do these

x2+7x+12

  1. Two numbers that multiply to 12 and add to 7.
  2. Factor pairs of 12: 1 and 12, 2 and 6, 3 and 4.
  3. 3 + 4 = 7, so those are the two.

The answer is (x+3)(x+4).

Where students go wrong

The sign slip is the common one. When the constant is positive but the middle term is negative, as in x² − 11x + 30, both numbers have to be negative: −5 and −6, not 5 and 6. The other one is skipping the common factor. 3x² − 3x − 90 is not prime, it is 3(x − 6)(x + 5), and a student who dives straight at the trinomial will not find it.

Also called factorising trinomials or factoring simple quadratics.

What you can put on this worksheet

Both factors positive
r2+10r+25 (r+5)2
Both factors negative
r210r+25 (r5)2
One of each sign
x2+x30 (x5)(x+6)
Mix in some that do not factor
v2+3v+6 Not factorable

Questions about these worksheets

Yes. Every factoring trinomials (a = 1) 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 factoring trinomials (a = 1) 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 4: both factors positive, both factors negative, one of each sign and mix in some that do not factor. Tick as many as you want and set how many of each, or let it spread them evenly.

The sign slip is the common one. When the constant is positive but the middle term is negative, as in x² − 11x + 30, both numbers have to be negative: −5 and −6, not 5 and 6. The other one is skipping the common factor. 3x² − 3x − 90 is not prime, it is 3(x − 6)(x + 5), and a student who dives straight at the trinomial will not find it.