The last one might throw me off if I didn’t remember off hand that a^3+b^3 has a factoring—is there a reason one should be especially likely to mistake the others?
These are not intended to be hard factoring problems for LessWrong, as if there were such a thing. They’re hard factoring problems for most high school algebra students because none of them have a leading coefficient of 1, and because on all but the first you have to remember to look for common factors before they even look like something you can cope with. The first is mainly hard because most kids, when they even remember how to deal with the 4 at all, will try to factor it as (2x+c)(2x+c) and then give up.
These are not intended to be hard factoring problems for LessWrong, as if there were such a thing.
Successfully factor inferential distance into how hard it will be to convince people in your life of the following:
Probability is subjective
Science and its method are a social model for humans to avoid believing in untrue things, not a logically correct way to discover what is most likely true.
Absence of evidence is evidence of absence (only applies for those who were or will be in college)
Maybe the “completely” is inappropriate here? In my defense, that’s what textbooks at this level usually say when they mean “factor as far as possible using real, integer coefficients”.
blinks
The last one might throw me off if I didn’t remember off hand that a^3+b^3 has a factoring—is there a reason one should be especially likely to mistake the others?
These are not intended to be hard factoring problems for LessWrong, as if there were such a thing. They’re hard factoring problems for most high school algebra students because none of them have a leading coefficient of 1, and because on all but the first you have to remember to look for common factors before they even look like something you can cope with. The first is mainly hard because most kids, when they even remember how to deal with the 4 at all, will try to factor it as (2x+c)(2x+c) and then give up.
Successfully factor inferential distance into how hard it will be to convince people in your life of the following:
Probability is subjective
Science and its method are a social model for humans to avoid believing in untrue things, not a logically correct way to discover what is most likely true.
Absence of evidence is evidence of absence (only applies for those who were or will be in college)
Good luck!
Its roots will be multiples of the three complex cube roots of unity, so it can’t be factored in the reals.
Maybe the “completely” is inappropriate here? In my defense, that’s what textbooks at this level usually say when they mean “factor as far as possible using real, integer coefficients”.
All I was looking for was 2(z+2)(z^2-2z+4).