Dumb Question: When Factoring Do We List Negative Factors?

In summary, factorisation is generally defined for positive numbers and there is no advantage in considering negative factors. This is because if a number is negative, it can be factored by taking its positive value and putting a minus sign in front. Allowing negative factors would also mean losing uniqueness in prime factorisation, which is why prime numbers are defined as being greater than 1. Therefore, while it may seem like an unspoken rule, it is simply a practical decision that is rarely noticed.
  • #1
bballwaterboy
85
3
I only see positive factors in my book. Example: 2 and 2 are factors of 4. But aren't -2 and -2?

Is there some unspoken rule in math that only positive factors count? Thanks!
 
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  • #2
There is no advantage in considering negative factors. So, factorisation is generally defined for positive numbers. If n is negative (-10, say), then -n is positive. So, you simply factorise -n and then put a minus sign in front:

-10 = -(10) = -(2)(5)

The main problem if you allowed negative factors would be that you no longer have uniqueness of the prime factorisation. This is why the definition of a prime number (p) includes the condition that p > 1.

So, essentially this is an unspoken rule as nobody notices it very often!
 

1. Can you factor negative numbers?

Yes, negative numbers can be factored just like positive numbers. The same rules apply for factoring both positive and negative numbers.

2. Do I have to list negative factors when factoring?

No, it is not necessary to list negative factors when factoring. However, it is important to include all possible factors, whether they are positive or negative, to get the correct answer.

3. What is the difference between positive and negative factors?

The only difference between positive and negative factors is their sign. Positive factors have a plus sign (+) in front of them, while negative factors have a minus sign (-). Both types of factors can be used in factoring.

4. When should I use negative factors in factoring?

You should use negative factors in factoring when they are necessary to get the correct answer. In some cases, including negative factors can help simplify the factoring process or lead to a more accurate solution.

5. Can negative factors be used in all types of factoring?

Yes, negative factors can be used in all types of factoring, including factoring polynomials, binomials, and trinomials. They follow the same rules as positive factors and can be used interchangeably.

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