Factorization Calculator Examples

Quadratic Factorization Formula:

\[ ax² + bx + c = a(x - p)(x - q) \text{ where } p + q = -\frac{b}{a}, p \times q = \frac{c}{a} \]

Factored Form:

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1. What Is Quadratic Factorization?

Quadratic factorization is the process of expressing a quadratic equation (ax² + bx + c) as a product of two binomials. It helps find the roots of the equation and understand its behavior.

2. How The Calculator Works

The calculator uses the quadratic formula to find roots:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Where:

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

Explanation: The calculator finds roots (p and q) and expresses the equation in factored form a(x - p)(x - q).

3. Importance of Factorization

Details: Factoring quadratics is essential for solving equations, graphing parabolas, and understanding the behavior of quadratic functions in physics, engineering, and economics.

4. Using The Calculator

Tips: Enter coefficients a, b, and c. The calculator works for all real numbers, but only shows real roots (not complex).

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: The equation becomes linear (not quadratic). The calculator requires a ≠ 0.

Q2: What if there's no real roots?
A: The calculator will indicate when the discriminant (b²-4ac) is negative.

Q3: Can it handle fractions or decimals?
A: Yes, the calculator accepts any real numbers including fractions and decimals.

Q4: What about perfect square trinomials?
A: The calculator automatically detects and factors perfect squares correctly.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places for clarity.