Factoring Polynomials Practice

Free Interactive Algebra Tool

Factor polynomial expressions one step at a time. Practice finding a greatest common factor, factoring trinomials, recognizing a difference of squares, and using the AC method.

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Learn How to Factor Polynomials Step by Step

Review greatest common factors, trinomial patterns, difference of squares, and the AC method with worked examples.

Read the Factoring Polynomials Guide

How It Works

Rewrite the Polynomial as a Product

Factoring reverses multiplication. Look for a common factor first, identify the polynomial pattern, and then build factors that multiply back to the original expression.

Check for a GCF

Determine whether every term shares a numerical or variable factor.

Identify the Pattern

Decide whether the expression is a trinomial, difference of squares, or another factorable form.

Build the Factors

Enter each algebraic step and use the required product and sum relationships.

Verify the Result

Multiply the factors to confirm that they produce the original polynomial.

Interactive Practice

Factor Each Polynomial

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Factoring Type

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Factor the Polynomial

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Factor the polynomial completely, showing each required step.

x² + 7x + 12

Find two integers whose product is 12 and whose sum is 7.

0 steps completed Enter one valid factoring step at a time.

Work One Step at a Time

Find the Required Number Pair

Current Step

Current Problem

x² + 7x + 12

Start x² + 7x + 12

Enter your answer to begin factoring.

Keep This Nearby

Factoring Polynomials Reference

Always check for a GCF first.

Greatest Common Factor Factor out the largest expression shared by every term. 6x² + 9x = 3x(2x + 3)

Monic Trinomial Find two numbers that multiply to c and add to b. x² + 7x + 12 = (x + 3)(x + 4)

Difference of Squares Use a² − b² = (a − b)(a + b). x² − 25 = (x − 5)(x + 5)

AC Method Find two numbers that multiply to ac and add to b. 6x² + 11x + 3

Factor by Grouping Group four terms and factor the GCF from each pair. 6x² + 9x + 2x + 3

Verify the Factors Multiply the factors to recover the original polynomial. (x + 3)(x + 4) = x² + 7x + 12

Key Reminders

Avoid Common Factoring Mistakes

Check the signs, look for a common factor, and make sure your factors multiply back to the original polynomial.

Check for a GCF First

Before using another method, determine whether all terms share a common numerical or variable factor.

8x² + 12x = 4x(2x + 3)

Use Both Conditions

A number pair must satisfy both the required product and the required sum.

3 · 4 = 12 and 3 + 4 = 7

Watch Negative Signs

The product determines whether the signs match, while the sum determines which sign is larger.

x² − x − 12 = (x − 4)(x + 3)

Factor Completely

Continue until none of the remaining factors can be factored further.

2x² − 18 = 2(x − 3)(x + 3)

Keep Learning

Review the Complete Factoring Process

Study greatest common factors, trinomial patterns, difference of squares, the AC method, and complete worked examples in the companion guide.