In Exercises 1–68, factor completely, or state that the polynomial is prime. 16y² − 4y − 2

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 methods include factoring out the greatest common factor, using the difference of squares, and applying the quadratic formula for quadratic polynomials.

Quadratic Polynomials

A quadratic polynomial is a polynomial of degree two, typically expressed in the form ax² + bx + c, where a, b, and c are constants. Understanding the structure of quadratic polynomials is crucial for identifying their factors. The roots of the polynomial can be found using factoring, completing the square, or the quadratic formula.

Prime Polynomials

A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials with real coefficients. Recognizing whether a polynomial is prime is important in algebra, as it determines the methods available for solving equations. If a polynomial cannot be factored, it may require numerical methods or graphing to find its roots.