Factoring

Factoring (or factorisation) rewrites an algebraic expression as a product of simpler expressions called factors. For polynomials, common patterns include:

• Common factor: $6x^2 + 9x = 3x(2x + 3)$.
• Difference of squares: $a^2 - b^2 = (a-b)(a+b)$.
• Perfect square trinomial: $a^2 + 2ab + b^2 = (a+b)^2$.
• Quadratic with integer roots: $x^2 + 5x + 6 = (x+2)(x+3)$ — find two numbers multiplying to $c$ and adding to $b$.

Factoring is the fastest way to find roots (set each factor to zero) and is essential for simplifying rational expressions. When integer factoring is impossible, fall back to the quadratic formula or completing the square.