1. What is Quadratic Factoring?

Factoring is the process of breaking down a quadratic equation into simpler multiplicative components. The factored form reveals the roots (solutions) of the equation directly.

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 calculator finds the roots (r₁ and r₂) and expresses the quadratic 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 complex algebraic expressions. It's fundamental in algebra and calculus.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c. The calculator will return the factored form or indicate if complex roots exist.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex roots?
A: The calculator will indicate that the quadratic cannot be factored with real numbers. Complex roots occur when the discriminant (b² - 4ac) is negative.

Q2: What if a = 0?
A: The equation becomes linear (not quadratic). The calculator requires a ≠ 0.

Q3: Can all quadratics be factored?
A: All quadratics can be factored, but some require complex numbers. Over real numbers, only quadratics with non-negative discriminants can be factored.

Q4: What about perfect square trinomials?
A: The calculator handles all cases, including perfect squares which result in repeated roots (r₁ = r₂).

Q5: How precise are the results?
A: Results are calculated with high precision, but displayed with up to 4 decimal places for readability.