Problem 107 - College Algebra

Question

What does it mean to factor completely?

Step-by-Step Solution

Answer

Complete factoring means breaking down an expression into a product of irreducible or simplest factors where further factoring is not possible. It simplifies the function or expressions and assists in their solutions.

Step 1: Define Factoring

Factoring is a crucial mathematical process where an expression is broken down into a product of smaller or simpler expressions. If the expression is a polynomial, factoring refers to rewriting the polynomial as a product of factor polynomials.

Step 2: Explain Complete Factoring

When we factor completely, we take factoring a step further. Rather than stopping partway, we continue factoring until no further factoring is possible. In other words, an expression is factored completely when the factors cannot be factored further.

Step 3: Importance of Complete Factoring

Factoring completely is important because it provides the simplest form of an expression, making it easier to solve or evaluate functions, find roots of the equations, simplify complex expressions, and understand relationships between variables in an equation.