Show that the polynomial `x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3)` is divisible by `x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot`

Explanation

To show that the polynomial \( f(x) = x^{4p} + x^{4q+1} + x^{4r+2} + x^{4s+3} \) is divisible by \( x^3 + x^2 + x + 1 \), we can use the Factor Theorem. The polynomial \( x^3 + x^2 + x + 1 \) has roots which are the fourth roots of unity, specifically \( 1, i, -i \) (where \( i = \sqrt{-1} \)).

### Step-by-Step Solution:

1. **Identify the Polynomial**:
We start with the polynomial:
\[
f(x) = x^{4p} + x^{4q+1} + x^{4r+2} + x^{4s+3}
...