In Exercises 23–48, factor completely, or state that the polynomial is prime. 2x³ - 8x

Key Concepts

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of its factors. This process often includes identifying common factors, applying special factoring techniques like difference of squares, or using methods such as grouping. Understanding how to factor is essential for simplifying expressions and solving polynomial equations.

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or terms without leaving a remainder. In polynomial expressions, finding the GCF allows for simplification by factoring it out, which can make the remaining polynomial easier to work with. Recognizing the GCF is a crucial first step in the factoring process.

Prime Polynomials

A prime polynomial is a polynomial that cannot be factored into simpler polynomials with rational coefficients. Identifying whether a polynomial is prime is important in algebra, as it determines whether further simplification is possible. Understanding the criteria for primality helps in recognizing when a polynomial is already in its simplest form.