1. What is Quadratic Factoring?

Factoring is the process of breaking down a quadratic equation into simpler multiplicative components. The standard form ax² + bx + c can be expressed as a product of two binomials: a(x - r₁)(x - r₂), where r₁ and r₂ are the roots of the 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 (solutions) of the quadratic equation and uses them to construct the factored form.

3. Importance of Factoring

Details: Factoring is essential for solving quadratic equations, graphing parabolas, and simplifying complex algebraic expressions. It's a fundamental skill in algebra with applications in physics, engineering, and economics.

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. For complex roots, it will indicate that factoring isn't possible with real numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, the equation is linear, not quadratic. The calculator requires a non-zero value for a.

Q2: Why does it say "Cannot factor"?
A: This happens when the discriminant (b² - 4ac) is negative, resulting in complex roots that can't be expressed in real factored form.

Q3: Can it factor perfect square trinomials?
A: Yes, the calculator handles all types of factorable quadratic expressions, including perfect squares.

Q4: What about irrational roots?
A: The calculator provides exact factored form with irrational roots when possible.

Q5: How accurate are the results?
A: Results are mathematically precise, though displayed with limited decimal places for readability.