Question

5
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if $p - 1$ is a factor of $p^4 + p^2 + p - k$, the value of $k$ is

Explanation:

Step1: Apply Factor Theorem

If $p-1$ is a factor, substitute $p=1$ into the polynomial and set it equal to 0:
$1^4 + 1^2 + 1 - k = 0$

Step2: Simplify the equation

Calculate the sum of the constants:
$1 + 1 + 1 - k = 0$
$3 - k = 0$

Step3: Solve for k

Rearrange to isolate $k$:
$k = 3$

Answer:

3