Factoring trinomials (a > 1) worksheet

Every question on this sheet has a leading coefficient greater than 1, so students have to split the middle term rather than just find two numbers. Pick how many you want and print. Every sheet is different.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Factoring Trinomials (a > 1) Date Period Factor each completely. $14 a^{2} - 79 a + 72$ $28 b^{2} + 31 b - 72$ $105 a^{2} - 303 a + 216$ $14 m^{2} + 108 m - 162$ $7 n^{2} + 64 n + 64$ $28 y^{2} + 31 y - 72$ $14 n^{2} + 79 n + 72$ $21 x^{2} - 29 x - 72$ $28 a^{2} + 99 a + 81$ $28 m^{2} + 31 m - 72$ $84 x^{2} - 320 x + 256$ $14 y^{2} + 47 y - 72$ $14 y^{2} - 79 y + 72$ $14 v^{2} + 47 v - 72$ $35 k^{2} + 325 k + 360$ $84 m^{2} + 128 m - 256$ $112 x^{2} + 380 x + 288$ $14 n^{2} - 47 n - 72$ $28 a^{2} - 99 a + 81$ $14 m^{2} + 47 m - 72$ 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.

$14 a^{2} - 79 a + 72$
$28 b^{2} + 31 b - 72$
$105 a^{2} - 303 a + 216$
$14 m^{2} + 108 m - 162$
$7 n^{2} + 64 n + 64$
$28 y^{2} + 31 y - 72$
$14 n^{2} + 79 n + 72$
$21 x^{2} - 29 x - 72$
$28 a^{2} + 99 a + 81$
$28 m^{2} + 31 m - 72$
$84 x^{2} - 320 x + 256$
$14 y^{2} + 47 y - 72$
$14 y^{2} - 79 y + 72$
$14 v^{2} + 47 v - 72$
$35 k^{2} + 325 k + 360$
$84 m^{2} + 128 m - 256$
$112 x^{2} + 380 x + 288$
$14 n^{2} - 47 n - 72$
$28 a^{2} - 99 a + 81$
$14 m^{2} + 47 m - 72$



Sigma Prep · sigmaprep.io/worksheets Name Factoring Trinomials (a > 1)Answer keyVersion 1 Date Period Factor each completely. $14 a^{2} - 79 a + 72$ $(2 a - 9) (7 a - 8)$ $28 b^{2} + 31 b - 72$ $(7 b - 8) (4 b + 9)$ $105 a^{2} - 303 a + 216$ $3 (7 a - 9) (5 a - 8)$ $14 m^{2} + 108 m - 162$ $2 (7 m - 9) (m + 9)$ $7 n^{2} + 64 n + 64$ $(n + 8) (7 n + 8)$ $28 y^{2} + 31 y - 72$ $(7 y - 8) (4 y + 9)$ $14 n^{2} + 79 n + 72$ $(7 n + 8) (2 n + 9)$ $21 x^{2} - 29 x - 72$ $(3 x - 8) (7 x + 9)$ $28 a^{2} + 99 a + 81$ $(4 a + 9) (7 a + 9)$ $28 m^{2} + 31 m - 72$ $(7 m - 8) (4 m + 9)$ $84 x^{2} - 320 x + 256$ $4 (3 x - 8) (7 x - 8)$ $14 y^{2} + 47 y - 72$ $(7 y - 8) (2 y + 9)$ $14 y^{2} - 79 y + 72$ $(2 y - 9) (7 y - 8)$ $14 v^{2} + 47 v - 72$ $(7 v - 8) (2 v + 9)$ $35 k^{2} + 325 k + 360$ $5 (k + 8) (7 k + 9)$ $84 m^{2} + 128 m - 256$ $4 (7 m - 8) (3 m + 8)$ $112 x^{2} + 380 x + 288$ $4 (7 x + 8) (4 x + 9)$ $14 n^{2} - 47 n - 72$ $(2 n - 9) (7 n + 8)$ $28 a^{2} - 99 a + 81$ $(4 a - 9) (7 a - 9)$ $14 m^{2} + 47 m - 72$ $(7 m - 8) (2 m + 9)$ 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.

$14 a^{2} - 79 a + 72$ $(2 a - 9) (7 a - 8)$
$28 b^{2} + 31 b - 72$ $(7 b - 8) (4 b + 9)$
$105 a^{2} - 303 a + 216$ $3 (7 a - 9) (5 a - 8)$
$14 m^{2} + 108 m - 162$ $2 (7 m - 9) (m + 9)$
$7 n^{2} + 64 n + 64$ $(n + 8) (7 n + 8)$
$28 y^{2} + 31 y - 72$ $(7 y - 8) (4 y + 9)$
$14 n^{2} + 79 n + 72$ $(7 n + 8) (2 n + 9)$
$21 x^{2} - 29 x - 72$ $(3 x - 8) (7 x + 9)$
$28 a^{2} + 99 a + 81$ $(4 a + 9) (7 a + 9)$
$28 m^{2} + 31 m - 72$ $(7 m - 8) (4 m + 9)$
$84 x^{2} - 320 x + 256$ $4 (3 x - 8) (7 x - 8)$
$14 y^{2} + 47 y - 72$ $(7 y - 8) (2 y + 9)$
$14 y^{2} - 79 y + 72$ $(2 y - 9) (7 y - 8)$
$14 v^{2} + 47 v - 72$ $(7 v - 8) (2 v + 9)$
$35 k^{2} + 325 k + 360$ $5 (k + 8) (7 k + 9)$
$84 m^{2} + 128 m - 256$ $4 (7 m - 8) (3 m + 8)$
$112 x^{2} + 380 x + 288$ $4 (7 x + 8) (4 x + 9)$
$14 n^{2} - 47 n - 72$ $(2 n - 9) (7 n + 8)$
$28 a^{2} - 99 a + 81$ $(4 a - 9) (7 a - 9)$
$14 m^{2} + 47 m - 72$ $(7 m - 8) (2 m + 9)$

How to do these

$2 x^{2} + 7 x + 3$

Multiply the ends: 2 times 3 is 6.
Two numbers that multiply to 6 and add to 7: 1 and 6.
Split the middle: 2x² + x + 6x + 3, then group.

The answer is $(2 x + 1) (x + 3)$ .

Where students go wrong

Most students try to guess the two binomials and give up when the first few guesses fail. Splitting the middle term is not a trick, it is the reliable method: multiply the first and last coefficients, find two numbers that multiply to that and add to the middle, then factor by grouping. It works every time, including when the answer is ugly.

Also called the AC method, splitting the middle term or factoring hard trinomials.

What you can put on this worksheet

Positive constant: $10 v^{2} + 13 v + 4$ → $(2 v + 1) (5 v + 4)$
Negative constant: $5 v^{2} - 28 v - 49$ → $(v - 7) (5 v + 7)$
Mix in some that do not factor: $3 v^{2} + v - 6$ → 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 3: positive constant, negative constant 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 trinomials (a > 1) worksheet

Select your difficulty

Factoring Trinomials (a > 1)

Factoring Trinomials (a > 1)Answer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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