Factoring Calculator Examples

Quadratic Factoring Formula:

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

Factored Form:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Quadratic Factoring?

Quadratic factoring is the process of breaking down a quadratic equation into the product of two binomials. It's a fundamental technique in algebra that helps solve quadratic equations and analyze their properties.

2. How Does the Calculator Work?

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 the roots (p and q) using the quadratic formula, then expresses the original quadratic in factored form as a(x - p)(x - q).

3. Importance of Factoring Quadratics

Details: Factoring quadratics is essential for solving equations, finding roots/x-intercepts, analyzing graphs of parabolas, and simplifying complex algebraic expressions.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation in the form ax² + bx + c. The calculator will display the factored form if real roots exist.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "Cannot be factored"?
A: This means the quadratic has no real roots (negative discriminant). You may need to use complex numbers.

Q2: Why is the factored form useful?
A: It immediately shows the roots of the equation and helps analyze the parabola's x-intercepts.

Q3: What if a ≠ 1?
A: The calculator handles all real values of a (except zero). The factored form will include the leading coefficient.

Q4: Can this calculator solve perfect square trinomials?
A: Yes, it will correctly factor them into identical binomials (x - p)².

Q5: What about quadratics that can't be factored nicely?
A: The calculator provides exact decimal solutions, which may include irrational numbers.