Answer:
[tex]k=3[/tex]
Explanations:
Given the polynomial function expressed as:
[tex]p^4+p^2+p-k[/tex]
If p - 1 is a factor, then one of the zeros of the polynomial will be derived as shown:
[tex]\begin{gathered} p-1=0 \\ p=0+1 \\ p=1 \end{gathered}[/tex]
This shows that one of the zeros of the expression is p = 1. Substitute this value into the polynomial function, we will have:
[tex]\begin{gathered} p^4+p^2+p-k=0 \\ 1^4+1^2+1-k=0 \\ 1+1+1-k=0 \\ 3-k=0 \\ k=0+3 \\ k=3 \end{gathered}[/tex]
This shows that the value of k if (p-1) is a factor of the polynomial is 3
