1. What is Trinomial Factoring?

Trinomial factoring is the process of breaking down a quadratic expression of the form ax² + bx + c into a product of two binomials. This helps find the roots (solutions) of the quadratic equation.

2. How Does the Calculator Work?

The calculator uses the quadratic formula to find roots:

Where:

• \( a \) — Coefficient of x² term
• \( b \) — Coefficient of x term
• \( c \) — Constant term

Explanation: The calculator finds the roots (r₁ and r₂) and expresses the original trinomial in its factored form a(x - r₁)(x - r₂).

3. Importance of Factoring

Details: Factoring trinomials is essential for solving quadratic equations, graphing parabolas, and simplifying algebraic expressions in calculus and higher mathematics.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will return the factored form if real roots exist.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "No real roots"?
A: This means the discriminant (b² - 4ac) is negative, indicating complex roots that this calculator doesn't display.

Q2: Can I factor perfect square trinomials?
A: Yes, the calculator will return identical roots for perfect squares (e.g., x² + 4x + 4 becomes (x + 2)²).

Q3: What if a = 1?
A: The calculator works the same way, but the factored form will be simpler (e.g., x² + 5x + 6 = (x + 2)(x + 3)).

Q4: How precise are the results?
A: Roots are rounded to 4 decimal places for readability.

Q5: Can this solve cubic or higher equations?
A: No, this calculator only handles quadratic (degree 2) trinomials.