Question

If p − 1 is a factor of p4 + p2 + p − k, the value of k is

Answer 1

Hello,


--------4----3----2----1----0
.........1.....0.....1.....1.....-k
p=1..........1.....1.....2 ....3
.........1.....1.....2.....3.....0

==>-k+3=0==>k=3

Answer 2

k = 3.

Explanation:

If p-1 is a factor of the polynomial, that is

`p^4+p^2+p-k = (p-1)q(p)`

with q(p) be another polynomial. Then with p=1 the polynomial is equal to 0. So,

`1^4+1^2+1-k = 0`

`1+1+1-k = 0`

`3-k = 0`

`k = 3`.