Question

14Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.If p- 1 is a factor of pf + p2 + p-k, the value of kisResetNext

Answer 1

`k=3`

Explanations:

Given the polynomial function expressed as:

`p^4+p^2+p-k`

If p - 1 is a factor, then one of the zeros of the polynomial will be derived as shown:

`\begin{gathered} p-1=0 \\ p=0+1 \\ p=1 \end{gathered}`

This shows that one of the zeros of the expression is p = 1. Substitute this value into the polynomial function, we will have:

`\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}`

This shows that the value of k if (p-1) is a factor of the polynomial is 3