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anyanavicka [17]
3 years ago
15

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

Mathematics
2 answers:
amid [387]3 years ago
6 0
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

lesantik [10]3 years ago
3 0

Answer:

k = 3.

Step-by-step 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.

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