Factor completely, or state that the polynomial is prime. 15x^3+3x^2

Key Concepts

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials or monomials. This process is essential for simplifying expressions and solving equations. Common techniques include factoring out the greatest common factor (GCF), using special products, and applying methods like grouping or the quadratic formula for higher-degree polynomials.

Greatest Common Factor (GCF)

The greatest common factor (GCF) of a set of terms is the largest expression that divides each term without leaving a remainder. Identifying the GCF is a crucial first step in factoring polynomials, as it allows for simplification by factoring out the GCF, making the remaining polynomial easier to work with.

Prime Polynomials

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials with real coefficients. Recognizing prime polynomials is important in algebra, as it indicates that the polynomial cannot be simplified further, which is essential for determining the solutions to equations involving the polynomial.