Problem 133 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Step-by-Step Solution

Answer

The statement makes sense, as factoring out the greatest common factor initially simplifies the problem and makes it easier to factor what remains, assuming the remaining part is not a prime number.

Step 1: Interpretation of the statement

The statement implies that first factoring out the greatest common factor from a number or an expression simplifies the subsequent factoring of what remains. The assumption part of the statement posits that the remaining factor, after factoring out the greatest common factor, is not a prime number.

Step 2: Understanding factoring and prime numbers

Factoring is the process of breaking down numbers or expressions into the product of their basic units or factors. In numbers, the most basic factors are the prime numbers. They are numbers with only two distinct positive divisors, 1 and the number itself. So, when a number or an expression has been factored by taking out the greatest common factor, what remains may or may not be a prime number.

Step 3: Validating the statement

Now, considering the process of factoring, it is easier to deal with smaller numbers or simpler expressions. So, by initially factoring out the greatest common factor, we essentially simplify the problem, making it easier to determine how to factor the remaining part. Thus, the statement makes sense and is logically correct.