In Exercises 93–100, factor completely. x² − 6/25 + 1/5 x

Key Concepts

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting them as a product of two binomials. This process is essential for simplifying expressions and solving equations. The standard form of a quadratic is ax² + bx + c, and the goal is to express it in the form (px + q)(rx + s). Recognizing patterns, such as perfect squares or the difference of squares, can aid in this process.

Common Denominators

In the given expression, the terms involve fractions, which require a common denominator for simplification. A common denominator allows us to combine or manipulate fractions effectively. In this case, the denominators are 25 and 5, and finding a common denominator helps in rewriting the expression in a more manageable form, facilitating the factoring process.

Completing the Square

Completing the square is a method used to transform a quadratic expression into a perfect square trinomial. This technique is particularly useful for factoring and solving quadratics. By rearranging the expression and adding/subtracting the necessary constant, we can express it in the form (x - p)² = q, which simplifies the factoring process and aids in finding the roots of the equation.