In Exercises 1–68, factor completely, or state that the polynomial is prime. 6bx² + 6by²

Key Concepts

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial expression as a product of simpler polynomials. This process is essential for simplifying expressions and solving equations. Common techniques include factoring out the greatest common factor (GCF), using special products like the difference of squares, and applying the quadratic formula when applicable.

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, identifying the GCF allows for simplification by factoring it out, which can make the remaining polynomial easier to work with. For example, in the expression 6bx² + 6by², the GCF is 6b.

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 crucial in algebra, as it indicates that the polynomial cannot be simplified further. In the case of 6bx² + 6by², after factoring out the GCF, the remaining expression may or may not be prime, depending on its structure.