Factoring Trinomials Calculator

Factoring is the process of breaking down a polynomial into simpler expressions that multiply together. Whether you need to factor a simple trinomial like x² + 5x + 6 or use advanced techniques like grouping or the difference of squares, our calculator shows you each step clearly. Understanding factoring is critical for solving quadratic equations and simplifying algebraic expressions.

How It Works

Enter your equation or expression into the solver above and click "Solve." Our system first attempts a deterministic verification using a symbolic math engine for guaranteed accuracy. If verified, you will see a Verified badge next to the answer.

Example Problem

x² + 7x + 12

Step-by-Step Solution

Identify: a = 1, b = 7, c = 12
Find two numbers that multiply to 12 and add to 7: 3 and 4
Write the factored form: (x + 3)(x + 4)

Final Answer: (x + 3)(x + 4)

Frequently Asked Questions

How do you factor a trinomial?

For ax² + bx + c, find two numbers that multiply to a*c and add to b. Use these to split the middle term and factor by grouping.

What is the difference of squares?

A difference of squares has the form a² - b² and factors as (a + b)(a - b). For example, x² - 9 = (x + 3)(x - 3).

What if the trinomial cannot be factored?

If no integer pair works, the polynomial is prime over the integers. You can still find roots using the quadratic formula.

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