Question

If p-1 is a factor of (p^4)+(p^2)+p-k. Then what is the value of K?

I will give a medal!!

Answer 1

@perl

Answer 2

lets see

Answer 3

Suppose we have the function
f(p) = (p^4)+(p^2)+p-k

if p -1 is a factor of (p^4)+(p^2)+p-k
then
f(1) = 0
so plug in 1

Answer 4

not quite , i wrote
f(1) = 0

Answer 5

so 0=(1^4)+(1^2)+1-k

Answer 6

yes that looks better

Answer 7

so would it be K=3?

Answer 8

Thank you @perl

Answer 9

the intuition here is if i say
p-1 is a factor of (p^4)+(p^2)+p-k
that means

(p^4)+(p^2)+p-k = (p - 1 ) * ( cubic expression in p )

then it makes sense that if p =1 , you will get zero
( 1-1) * ( something) = 0