Simple
\(x^2 + 5x + 6 = (x + 2)(x + 3)\)
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Theory & Formula
Factoring is the process of breaking down a polynomial into simpler expressions (factors) that multiply together to give the original polynomial.
For quadratic expressions, factoring reveals the roots (zeros) of the polynomial:
- Standard form: ax² + bx + c
- Factored form: a(x - r₁)(x - r₂) where r₁ and r₂ are the roots
- Special cases: Perfect squares, difference of squares
- Not all quadratics factor nicely over integers
\(ax^2 + bx + c = a(x - r_1)(x - r_2)\)
Worked Examples
Difference of Squares
\(x^2 - 9 = (x - 3)(x + 3)\)
Perfect Square
\(x^2 + 6x + 9 = (x + 3)^2\)
Leading Coefficient
\(2x^2 - 8x + 6 = 2(x - 1)(x - 3)\)