1. What is the Factoring Formula?

The factoring formula \( factored = a(x + p)(x + q) \) represents a quadratic expression in its factored form, where 'a' is the coefficient, and p and q are the roots of the equation.

2. How Does the Calculator Work?

The calculator uses the factoring formula:

Where:

• \( a \) — Leading coefficient (unitless)
• \( x \) — Variable in the expression
• \( p \) — First root (unitless)
• \( q \) — Second root (unitless)

Explanation: The formula converts a quadratic expression into its factored form, which reveals the roots of the equation directly.

3. Importance of Factoring

Details: Factoring is essential for solving quadratic equations, finding roots, graphing parabolas, and simplifying complex algebraic expressions.

4. Using the Calculator

Tips: Enter the coefficient (a), variable (typically x), and the two roots (p and q). The calculator will generate the factored form of the expression.

5. Frequently Asked Questions (FAQ)

Q1: What if my quadratic doesn't factor neatly?
A: Some quadratics require the quadratic formula or completing the square if they don't factor into integer roots.

Q2: Can this calculator handle complex roots?
A: No, this calculator is designed for real roots only. Complex roots require different representation.

Q3: How does the coefficient 'a' affect the factored form?
A: The coefficient 'a' scales the entire expression and affects the parabola's width and direction.

Q4: What's the difference between factored form and standard form?
A: Factored form reveals roots directly, while standard form (ax²+bx+c) is better for identifying the y-intercept.

Q5: Can I use letters other than x for the variable?
A: Yes, you can use any single-letter variable in the calculator (like y, z, etc.).