Question

factorise the polynomial x^3+1 as a product of degree 1 and degree 2 polynomial. Use this to help find all the prime divisors of n^3+1 for akk intergers n with 2<=n<=3

So i factorised it...but then idk how to use it to help me find the divisors?

Answer 1

yeah i did that....but how do i use that to help me find the divisors?

Answer 2

can you find the divisors without using that ?

Answer 3

btw, divisor is just another name for factor

Answer 4

so plug in n = 2 and n =3

2^3 + 1 = ( 2 + 1 ) ( 2^2 - 2 + 1) = 3* 3

3^3 + 1 = ( 3 + 1 ) ( 3^3 - 3 + 1 ) = 4* 7

Answer 5

it wants me to find all the prime divisors using it, so i think i will have to use it

Answer 6

yes you will have to use it because the question is asking you to

im asking whether you can find it without using that

Answer 7

Yeah i could find them...but i think that would be a long process. So i assume using the factorised version would speed things up?

Answer 8

the factorised version only speeds up when n is large

Answer 9

well when n is at its max allowed value i need the prime divisors of 1001

Answer 10

then factorised version really pays off

Answer 11

I feel like im being really stupid in not seeing how to use the factorised version?

Answer 12

still not seeing it ?

Answer 13

@perl gave you examples already

Answer 14

ohhhhhhhhhhhhhhhhhhh

Answer 15

you wana do another example for large n =1001 ?

Answer 16

this a nifty trick , if one less is a perfect cube

Answer 17

so when n = 10, you have (90+1)(10+1)=1001