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 of the equation and understand its behavior.

2. How Does the Calculator Work?

The calculator uses the quadratic formula to find roots:

Where:

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

Explanation: The roots found are then used to express the trinomial in its factored form a(x - r₁)(x - r₂).

3. Importance of Factoring

Details: Factoring 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 display the factored form if real roots exist.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "Cannot factor"?
A: This means the equation has complex roots (negative discriminant). The trinomial cannot be factored using real numbers.

Q2: What if a = 1?
A: The calculator works for any non-zero value of a. When a=1, the factored form simplifies to (x - r₁)(x - r₂).

Q3: How accurate are the results?
A: Results are accurate to 4 decimal places. For exact fractions, manual calculation may be needed.

Q4: Can this solve perfect square trinomials?
A: Yes, perfect squares will show identical roots (r₁ = r₂) resulting in (x - r)² form.

Q5: What about non-quadratic trinomials?
A: This calculator only handles quadratic trinomials (degree 2). Higher-degree polynomials require different methods.