Yes, factors can be negative if the number being factored has negative factors, and factorization includes both positive and negative divisors.
Factors can be negative. When factoring a number, both positive and negative integers that divide the given number without leaving a remainder are considered factors.
For example, when factoring -12, the positive factors include 1, 2, 3, 4, 6, and 12, while the negative factors are -1, -2, -3, -4, -6, and -12.
This is because multiplying any of these negative factors by the original number yields a product of -12. In general, the concept of factors extends beyond positive integers, encompassing negative integers as well.
Divisors can be any number used to divide another number, while factors are divisors that divide the number without a remainder, hence, all factors are divisors, but not all divisors are factors.
Recognizing and incorporating negative factors is crucial in various mathematical applications, such as solving equations, understanding the complete set of divisors for a number, and working with expressions that involve both positive and negative terms. The inclusion of negative factors provides a more comprehensive and accurate representation of the relationships between numbers.