Algebra Practice Test

When factoring the expression 2x² - 10x + 12, what is the first step?

1. Identify common factors

2. Use the quadratic formula

3. Check if it can be simplified to a monomial

4. Rearrange the equation

The correct answer is: Identify common factors

The first step in factoring the expression 2x² - 10x + 12 is to identify common factors. This is crucial because it allows us to simplify the expression before seeking further factors. In this case, all the terms in the expression share a common factor of 2. By factoring out this common factor, we can rewrite the expression as 2(x² - 5x + 6). This simplification makes it easier to identify the roots or to factor the quadratic further. Identifying common factors is a foundational step in factoring polynomials, as it reduces the complexity of the expression we are working with. Once we've simplified it by removing the common factor, we can then factor the quadratic within the parentheses further, which may involve finding two numbers that multiply to the constant term and add up to the coefficient of the linear term. In contrast, using the quadratic formula would be a later step if factoring directly does not yield easily recognizable factors. Checking if it can be simplified to a monomial is not applicable here since the expression is a polynomial with multiple terms. Rearranging the equation isn’t necessary at this stage, as we aim to factor the expression directly to find the roots or intercepts. Thus, recognizing and extracting