Factoring review worksheet: all techniques

The hard part of factoring is not any single method, it is deciding which one applies. This sheet mixes all of them, which is what a test does and what a sheet on one technique never asks. Tick the methods you have covered so far.



Sigma Prep · sigmaprep.io/worksheets Name Factoring Review Date Period Factor each completely. $v^{2} + 20 v + 99$ $a^{2} - 2 a - 120$ $63 p^{2} - 240 p + 192$ $5 x^{2} + 15 x - 140$ $25 n^{2} - 196$ $b^{2} + 22 b + 120$ $n^{2} + n - 132$ $35 p^{2} - 101 p + 72$ $6 b^{2} + 24 b - 72$ $25 n^{2} - 169$ $y^{2} + 21 y + 108$ $y^{2} + y - 110$ $105 a^{2} - 303 a + 216$ $6 m^{2} - 6 m - 180$ $98 x^{2} - 450$ $5 b^{2} + 110 b + 600$ $2 n^{2} - 2 n - 220$ $14 m^{2} + 144 m + 162$ $5 k^{2} + 20 k - 60$ $25 a^{2} - 196$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep



Sigma Prep · sigmaprep.io/worksheets Name Factoring ReviewAnswer keyVersion 1 Date Period Factor each completely. $v^{2} + 20 v + 99$ $(v + 9) (v + 11)$ $a^{2} - 2 a - 120$ $(a - 12) (a + 10)$ $63 p^{2} - 240 p + 192$ $3 (3 p - 8) (7 p - 8)$ $5 x^{2} + 15 x - 140$ $5 (x - 4) (x + 7)$ $25 n^{2} - 196$ $(5 n - 14) (5 n + 14)$ $b^{2} + 22 b + 120$ $(b + 10) (b + 12)$ $n^{2} + n - 132$ $(n - 11) (n + 12)$ $35 p^{2} - 101 p + 72$ $(7 p - 9) (5 p - 8)$ $6 b^{2} + 24 b - 72$ $6 (b - 2) (b + 6)$ $25 n^{2} - 169$ $(5 n - 13) (5 n + 13)$ $y^{2} + 21 y + 108$ $(y + 9) (y + 12)$ $y^{2} + y - 110$ $(y - 10) (y + 11)$ $105 a^{2} - 303 a + 216$ $3 (7 a - 9) (5 a - 8)$ $6 m^{2} - 6 m - 180$ $6 (m - 6) (m + 5)$ $98 x^{2} - 450$ $2 (7 x - 15) (7 x + 15)$ $5 b^{2} + 110 b + 600$ $5 (b + 10) (b + 12)$ $2 n^{2} - 2 n - 220$ $2 (n - 11) (n + 10)$ $14 m^{2} + 144 m + 162$ $2 (m + 9) (7 m + 9)$ $5 k^{2} + 20 k - 60$ $5 (k - 2) (k + 6)$ $25 a^{2} - 196$ $(5 a - 14) (5 a + 14)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

$3 x^{2} - 3 x - 90$

Always look for a common factor first: 3 comes out of every term.
That leaves x² − x − 30 inside.
Two numbers multiplying to −30 and adding to −1: −6 and 5.

The answer is $3 (x - 6) (x + 5)$ .

Where students go wrong

Reaching for the trinomial method straight away. The order matters: common factor first, then count the terms. Two terms means a difference of squares, three means a trinomial, four means grouping. Students who skip the common factor get an answer that looks finished and is not.

Also called mixed factoring or factoring practice, all methods.

What you can put on this worksheet

Both factors positive: $r^{2} + 10 r + 25$ → $(r + 5)^{2}$
Both factors negative: $r^{2} - 10 r + 25$ → $(r - 5)^{2}$
One of each sign: $x^{2} + x - 30$ → $(x - 5) (x + 6)$
Positive constant: $10 v^{2} + 13 v + 4$ → $(2 v + 1) (5 v + 4)$
Negative constant: $5 v^{2} - 28 v - 49$ → $(v - 7) (5 v + 7)$
Trinomial with a common factor: $2 v^{2} + 2 v - 40$ → $2 (v - 4) (v + 5)$
Common factor only: $25 v^{3} + 15 v^{2}$ → $5 v^{2} (5 v + 3)$
Difference of two squares: $9 v^{2} - 100$ → $(3 v - 10) (3 v + 10)$
Perfect square trinomial: $16 v^{2} + 8 v + 1$ → $(4 v + 1)^{2}$
Four terms: $14 v^{3} - 63 v^{2} + 18 v - 81$ → $(2 v - 9) (7 v^{2} + 9)$
Mix in some that do not factor: $v^{2} + 3 v + 6$ → Not factorable

Questions about these worksheets

Yes. Every factoring review worksheet: all techniques 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 review worksheet: all techniques 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 11: both factors positive, both factors negative, one of each sign, positive constant, negative constant, trinomial with a common factor, common factor only, difference of two squares, perfect square trinomial, four terms 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.

Factoring review worksheet: all techniques

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