Rewriting quadratic expressions in factored form involves breaking them down into simpler expressions (factors) that multiply together to create the original expression. Factoring is crucial for solving quadratic equations and understanding the behavior of polynomials. This process utilizes the zero product property and the greatest common factor (GCF) to group and manipulate terms, leading to trinomial factoring (for expressions with three terms) and single variable factoring (for expressions with only a squared variable). Factoring enables solving quadratic equations by identifying its roots (zeroes), while related mathematical tools like the quadratic formula and the discriminant provide insights into the nature of the solutions.
