Answer :
Final answer:
The correct answer is option a. −3 is a factor of 66 because it can be multiplied by the integer −22 to produce 66, demonstrating the multiplication rule that like signs (both negative in this case) result in a positive product. So, the correct option is a. Yes, because 66 = (−3)(−22).
Explanation:
The question asks whether −3 is a factor of 66. To determine if a number is a factor of another, we need to check if the first number can be multiplied by an integer to produce the second number.
Following the multiplication rules for signs, we know that when two negative numbers multiply, the result is a positive number, as in the example of (-4) x (-3) = 12. Similarly, if −3 were a factor of 66, multiplying it by some negative integer should result in 66.
Indeed, −3 multiplied by −22 equals 66, (−3)(−22) = 66. This is in accordance with the principle of multiplication that opposite signs result in a negative product, and like signs result in a positive product. Therefore, even though −3 is a negative number, it can be a factor when paired with another negative integer to produce a positive product.
So, the correct option is a. Yes, because 66 = (−3)(−22), meaning that −3 is indeed a factor of 66 because it can be multiplied by −22 (which is an integer) to produce 66.
