Is there a way to tell how to factor the denominator when doing a partial fraction?

Answer 1

An additional rule to dividing by 4 is that if the last 2 digits are divisible by 4, the entire number is. Ex: 724 is divisible by 4 because 24 is.

But, I think we need to clarify your question. Are you talking about partial fraction decomposition? If so, I'm betting your denominators are polynomials? Some polynomials are factorable, others are not. Focus on each denominator separately - as if they're distinct polynomials. Is it a difference of squares? The square of a sum? Sum/difference of cubes? None of these? Each factorable denominator can be identified by the attributes you've already studied.

It might help if you are more specific with your question, so we can better know how to assist you.

Answer 2

Use these basic rules:

Factor by 2 - if the number is even

Factor by 3 - the sum of the digits is divisible by 3, for example 741: 7 + 4 + 1 = 12, therefore it's divisible by 3.

Factor by 4 - if you divide it in half and the result is even, it's divisible by 4.

Factor by 5 - ends in 0 or 5

Factor by 6 - It satisfies the rule for 3's and it is even.

No rule for 7s

Factor by 8 - last 3 digits of the number are divisible by 8

Factor by 9 - Similar to 3s, sum of the digits are divisible by 9

Factor by 10 - ends in a 0