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• Printable Factoring Trinomials Worksheets in PDF: AC Method and Grouping Practice

Printable Factoring Trinomials Worksheets in PDF: AC Method and Grouping Practice

These free printable worksheets give algebra students practice factoring trinomials into two binomial factors. Each worksheet includes an answer key, so students can check their own results.

Problems range from simple trinomials, where the leading coefficient is 1, to trinomials in the form ax² + bx + c, where the leading coefficient is not 1. For more algebra practice, explore Brighterly’s algebra worksheets hub.

Factoring Trinomials Worksheets: Free Download

This topic is available as four downloadable worksheet files:

What Is a Trinomial?

A trinomial is a math expression with three terms, usually connected by plus or minus signs, such as x² + 4x + 3. Factoring a trinomial means rewriting it as the product of two binomials.

Factoring a Simple Trinomial (a = 1): The Sum-Product Method

When the leading coefficient is 1, factor by finding two numbers that multiply to the constant term and add up to the middle coefficient.

Worked Example: b² + 8b + 7

• Find two numbers that multiply to 7 and add to 8: 7 and 1.
• Write these as two binomials: (b + 7)(b + 1)

b² + 8b + 7 = (b + 7)(b + 1)

Factoring a Trinomial When a Is Not 1: The AC Method

When the leading coefficient (a) isn’t 1, use the AC method: multiply a and c, find two numbers that multiply to that product and add to b, then rewrite the middle term and factor by grouping.

Worked Example: 2x² + 7x + 3

• Multiply a and c: 2 × 3 = 6
• Find two numbers that multiply to 6 and add to 7: 6 and 1.
• Rewrite the middle term using these numbers: 2x² + 6x + 1x + 3
• Group the terms: (2x² + 6x) + (1x + 3)
• Factor each group: 2x(x + 3) + 1(x + 3)
• Factor out the common binomial: (2x + 1)(x + 3)

2x² + 7x + 3 = (2x + 1)(x + 3)

Factoring a Perfect Square Trinomial

Some trinomials are perfect squares, meaning they factor into two identical binomials.

Worked Example: b² + 16b + 64

• Find two numbers that multiply to 64 and add to 16: 8 and 8.
• Write these as two identical binomials: (b + 8)(b + 8)

b² + 16b + 64 = (b + 8)²

Quick Answer Check for This Worksheet’s Problems

• b² + 8b + 7 = (b + 7)(b + 1)
• n² − 11n + 10 = (n − 10)(n − 1)
• m² + m − 90 = (m + 10)(m − 9)
• n² + 4n − 12 = (n + 6)(n − 2)
• n² − 10n + 9 = (n − 9)(n − 1)
• b² + 16b + 64 = (b + 8)²

More Factoring and Polynomial Worksheets

Once your child is confident factoring trinomials, explore more of Brighterly’s algebra practice:

• Factoring Quadratics Worksheets
• Multiplying Polynomials Worksheet
• Factoring Polynomials Worksheets
• Factoring By Grouping Worksheets
• Solving Quadratic Equations By Factoring Worksheets
• Factoring Worksheets

What Students Practice With These Factoring Trinomials Worksheets

• Factoring simple trinomials using the sum-product method
• Factoring trinomials with a leading coefficient other than 1 using the ac method
• Recognizing and factoring perfect square trinomials
• Checking a factored answer by expanding it back out
• Checking work against an included answer key

Each worksheet includes an answer key, so students can check their own results without waiting for a teacher to grade the page. Practicing the sum-product method alongside the ac method gives students a reliable approach no matter what the leading coefficient of a trinomial happens to be.

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FAQ

What is the ac method for factoring trinomials?

The ac method is used when a trinomial’s leading coefficient isn’t 1. Multiply the leading coefficient (a) by the constant term (c), then find two numbers that multiply to that product and add to the middle coefficient (b). Rewrite the middle term using those two numbers, then factor the expression by grouping.

How do you factor a simple trinomial where a = 1?

When the leading coefficient is 1, find two numbers that multiply to the constant term and add up to the middle coefficient. Write those two numbers into two binomials, each paired with the variable. You can always check the answer by expanding the two binomials back out to confirm they match the original trinomial.

What is a perfect square trinomial?

A perfect square trinomial is a trinomial that factors into two identical binomials, such as b² + 16b + 64, which factors into (b + 8)². You can spot one by checking whether the first and last terms are perfect squares and whether the middle term equals twice the product of their square roots.

What grade level are these factoring trinomials worksheets for?

These worksheets are written for middle school and early high school algebra students, starting around grade 7 and continuing into Algebra 1. Problems begin with simple trinomials where the leading coefficient is 1 before moving into trinomials that require the ac method, matching how factoring is typically introduced in sequence.

Does this worksheet include an answer key?

Yes, this factoring trinomials worksheet includes an answer key at the end of the document. Students can check their own results as soon as they finish a problem, which helps them catch mistakes in a sum-product or ac-method step right away, instead of waiting for a teacher to grade the assignment.