Question

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

A) 2
B) 3
C) 4
D) 5

Answer 1

The student's question about the value of k when p-1 is a factor of p⁴ + p² + p - k is solved by substituting p = 1 into the equation, which gives the value of k as 3.

Step-by-step explanation:

The student's question is about finding the value of k given that p - 1 is a factor of p⁴ + p² + p - k. If p - 1 is a factor, then by factor theorem, plugging p = 1 into the equation should result in a value of 0 for the entire expression. Substituting p with 1 gives us 1⁴ + 1² + 1 - k = 0, which simplifies to 1 + 1 + 1 - k = 0. Therefore, 3 - k = 0, and solving for k gives us k = 3. So, the value of k is 3, which corresponds to choice B.