Final Answer:
This is determined by factoring each quadratic expression and identifying the common factor (x + 2). So, the correct option is x² 3x 2.
Explanation:
In the process of determining the correct option, we employ quadratic factoring to break down the given expressions into their constituent factors. Firstly, we factor each quadratic expression independently. For the expression x² + 7x + 10, its factors are determined as (x + 5)(x + 2). Moving on to x² + 4x + 4, its factors are (x + 2)(x + 2), and for x² + 3x + 2, the factors are found to be (x + 2)(x + 1). In the second step, we identify the common factor among these factored expressions, which is (x + 2). Consequently, the correct option is revealed as x² 3x 2.
Understanding how to factor quadratic expressions is crucial for problem-solving in algebra. This process facilitates the simplification of complex expressions and serves as a foundation for solving quadratic equations. By recognizing common factors, mathematicians can streamline equations and gain insights into the underlying structure of mathematical relationships.
Proficiency in quadratic factoring enhances problem-solving skills and lays the groundwork for tackling more advanced mathematical concepts. As such, the ability to factor quadratic expressions is a fundamental skill that empowers individuals to navigate and manipulate mathematical expressions effectively.