Algebra

Factoring Quadratic Equations

Formula

ax² + bx + c = a(x − r₁)(x − r₂)

What is Factoring Quadratic Equations?

A quadratic equation can be factored into the product of two binomials, where r₁ and r₂ are the roots. To factor, find two numbers that multiply to give a×c and add to give b.

Variables

a
a, b, c — Coefficients of the quadratic
r
r₁, r₂ — Roots of the equation

Worked Examples

Example 1

Factor x² + 7x + 12.

Solution:

Find two numbers that multiply to 12 and add to 7: 3 and 4. x² + 7x + 12 = (x + 3)(x + 4)

Frequently Asked Questions

Related Formulas

Quadratic Equation

x = (−b ± √(b² − 4ac)) / 2a

Linear Equation in Two Variables

ax + by + c = 0

Distance Formula

Distance = Speed × Time

Laws of Exponents

aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ / aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ

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