What does factoring an algebraic expression involve?

Factoring an algebraic expression involves breaking down the expression into simpler components, specifically into products of its factors. This process allows one to rewrite complex polynomials into ways that can reveal solutions or simplify calculations. When you factor an expression, you are finding all the possible roots or contributing simpler factors that, when multiplied together, return to the original expression.

For example, factoring the expression (x^2 - 5x + 6) results in ((x - 2)(x - 3)). Each factor represents a simpler component that makes up the original polynomial. This method is essential in solving equations or simplifying expressions, as it allows for easier manipulation and analysis.

In contrast, multiplying the expression by a constant changes its value rather than simplifying or breaking it down. Combining like terms involves rearranging and simplifying within an expression but does not necessarily break it down into factors. Dividing the expression into two equal parts does not reflect the essence of factoring; it's more about splitting the expression than finding its roots or simpler multiplicative forms.