Name: Factoring Trinomials Worksheet – When a is Not 1
SKU: 6331049a2834d87864108f02
Price: 39.99 USD
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About this resource

What's inside this resource

Factoring Trinomials (when a is Not 1) Solve and Match Worksheet This 9th-12th grade math worksheet focuses on factoring trinomials when the leading coefficient (a) is not 1. Students will solve 18 factoring problems and match their answers to a letter key. For each problem, students factor the trinomial, solve to find the solutions, and write the letter of the matching answer choice beneath the problem number. Letters are only used once across the 18 problems. This activity allows students to practice an essential Algebra 1 skill while reinforcing their understanding of solutions to a factored trinomial. The worksheet format is ideal for individual, pair, small group, or whole class work. Answer keys are included, making this worksheet teacher-friendly for use across various settings from public schools to homeschools.

What's included

Problems 1-9 on the first page: 3x² + 10x − 8, 4x² + 11x − 3, 5x² + 19x + 18, 6x² − 29x − 5, 2x² − 17x + 21, 7x² − 31x + 30, 5x² + 11x + 6, 2x² − 7x − 30 and 4x² − x − 14
A nine-letter answer bank for those problems, listing monic binomials from (x + 1) to (x − 5)
Problems 10-18 on the second page: 15x² − 26x + 8, 21x² + 17x + 2, 8x² + 30x + 25, 20x² − 96x + 27, 18x² − x − 4, 21x² − 11x − 6, 27x² + 66x − 16, 18x² + 21x − 49 and 9x² + 24x + 16
A second nine-letter bank for those problems, listing binomials with their own coefficients from (3x + 8) to (3x + 1)
A direction line stating that each letter will only be used one time
A two-page worked key giving the lettered match and both factors for all eighteen problems, for example (10x − 3)(2x − 9) for problem 13
Name and Per lines on the student pages and the ©EightGoneSideways2020 footer throughout

Resource types: Worksheets & Printables, Worksheets

In the classroom

Teaching tips & learning objectives

Learning objectives

Factor a trinomial whose leading coefficient is greater than 1, such as 3x² + 10x − 8 = (3x − 2)(x + 4)
Factor trinomials where both binomial factors carry a coefficient, as with 20x² − 96x + 27 = (10x − 3)(2x − 9)
Recognise a perfect square trinomial, as in 9x² + 24x + 16 = (3x + 4)(3x + 4)
Use a matching bank as a self-check, treating a letter that is already taken as a signal to revisit the working
Handle negative constant and middle terms confidently across signs, from 2x² − 7x − 30 to 7x² − 31x + 30

Teaching tips

The two pages are graded deliberately: on page one only one factor of each pair is monic, so the bank gives away the easier half, while page two's bank lists binomials that both carry coefficients
Because each letter is used exactly once, a student who finds a letter already taken knows immediately that one of the two answers is wrong — worth pointing out before they start, since it turns the sheet into its own feedback loop
Problem 18, 9x² + 24x + 16, factors as (3x + 4)(3x + 4), which makes it the natural example for spotting a perfect square trinomial before grinding through the general method
Problem 13, 20x² − 96x + 27, has the largest coefficients on the sheet and the most factor pairs to test, so it is the one worth modelling or leaving as an extension
The key prints both factors rather than the letter alone, so it can be used to mark the working as well as the matching

Skills covered

Factoring trinomials with a leading coefficient above 1 — every one of the eighteen problems has an x² coefficient between 2 and 27, so the simple sum-and-product method will not work.
Testing factor pairs systematically — problems such as 20x² − 96x + 27 and 27x² + 66x − 16 require working through the factor pairs of both the leading coefficient and the constant.
Managing signs in a factorisation — the set mixes all four sign patterns, from 5x² + 19x + 18 through 6x² − 29x − 5 to 7x² − 31x + 30.
Recognising a perfect square trinomial — 9x² + 24x + 16 resolves to two identical factors, the only such case on the sheet.
Self-checking against a fixed bank — each lettered binomial is used exactly once across nine problems, so a clash reveals an error without a marker being involved.

Good to know

Questions teachers ask about this resource

How does the matching work when a trinomial has two factors?

The bank lists only one factor from each pair. On the first page it is always the monic one — (x + 4) for 3x² + 10x − 8, whose full factorisation is (3x − 2)(x + 4). On the second page the listed factor carries its own coefficient, as with (2x − 9) for 20x² − 96x + 27 = (10x − 3)(2x − 9).

Do the two pages differ in difficulty?

Yes, and the answer banks show how. Page one keeps one factor monic, so the coefficients stay small — 3x² + 10x − 8, 5x² + 11x + 6. Page two moves to expressions like 20x² − 96x + 27 and 27x² + 66x − 16, where both factors carry coefficients and far more factor pairs have to be tested.

What stops a student from guessing their way through the matching?

The direction that each letter will only be used one time. Nine problems share nine letters, so a wrong factorisation forces a clash somewhere else on the page and the student has to go back into the working rather than settle for a plausible-looking answer.