In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 12x + 36 − 49y²

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 identifying common factors, using the difference of squares, and applying the quadratic formula when necessary.

Difference of Squares

The difference of squares is a specific factoring pattern that applies to expressions of the form a² - b², which can be factored into (a + b)(a - b). In the given polynomial, recognizing the structure of a difference of squares is crucial for simplifying the expression effectively.

Quadratic Expressions

A quadratic expression is a polynomial of degree two, typically written in the form ax² + bx + c. Understanding the properties of quadratic expressions, including their graphs and roots, is vital for factoring them. In this case, recognizing that the expression can be rearranged into a quadratic form aids in the factoring process.