Original post by Matheen1
I know 8a) is just a 1 marker but how do I solve this?
I know 8a) is just a 1 marker but how do I solve this?
expand the right hand side (efficiently) and match the constant and linear terms (for instance). c is trivial and b isnt much harder.
(edited 11 months ago)
Original post by mqb2766
expand the right hand side (efficiently) and match the constant and linear terms (for instance). c is trivial and b isnt much harder.
Thanks I got it now b=-1 and c=1. But how would I go about solving 8b?
Original post by Matheen1
Thanks I got it now b=-1 and c=1. But how would I go about solving 8b?
Obviously part a) is a bit of a hint? So you want to show K is composite (not prime) so looking for a factor pair which is not 1,K ...
Also as a bit of a hint, you could have solved a by subbing n=0 to get c and n=1 to get b as the factorisation is valid, but they say n>2 so think about why.
(edited 11 months ago)
Original post by mqb2766
Obviously part a) is a bit of a hint? So you want to show K is composite (not prime) so looking for a factor pair which is not 1,K ...
Also as a bit of a hint, you could have solved a by subbing n=0 to get c and n=1 to get b as the factorisation is valid, but they say n>2 so think about why.
Also as a bit of a hint, you could have solved a by subbing n=0 to get c and n=1 to get b as the factorisation is valid, but they say n>2 so think about why.
I’m trying to understand what to do but I’m still struggling
Original post by Matheen1
I’m trying to understand what to do but I’m still struggling
Part a) factorises K. So its the product of two factors ...
(edited 11 months ago)
Following from mqb's hint.
You want to show 2 things really, in order of difficulty (imo) :
(1) n^3+1 has two factors other than 1 and itself.
(2) These two factors are distinct.
(1) is actually two mini parts - (i) it factorizes, and (ii) neither one could be 1 (and thus the other can't be K automatically).
(i) is done in (a).
(ii): the linear term is done. How do you show the quadratic term can't be 1?
(2) is really saying n^2-n+1 never equals to n+1.
To show*, well... try!
I think mqb's hint in #4 is quite good...
*I have intentionally use the word "show", because apparently the p-word scares people. They're really nothing more than writing an argumentative paragraph littered with alien symbols just for intimidation.
You want to show 2 things really, in order of difficulty (imo) :
(1) n^3+1 has two factors other than 1 and itself.
(2) These two factors are distinct.
(1) is actually two mini parts - (i) it factorizes, and (ii) neither one could be 1 (and thus the other can't be K automatically).
(i) is done in (a).
(ii): the linear term is done. How do you show the quadratic term can't be 1?
(2) is really saying n^2-n+1 never equals to n+1.
To show*, well... try!
I think mqb's hint in #4 is quite good...
*I have intentionally use the word "show", because apparently the p-word scares people. They're really nothing more than writing an argumentative paragraph littered with alien symbols just for intimidation.
(edited 11 months ago)
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