Question

Is (x + 1) a factor of x² + x³ + x + 1

Explanation please

Answer 1

To determine whether (x + 1) is a factor of x² + x³ + x + 1, we can use synthetic division or long division to divide x² + x³ + x + 1 by x + 1.

Using synthetic division, we can write:

-1 | 1 1 0 1
| -1 0 -0
| ___________
| 1 0 0 1

Since the remainder is not zero, we can conclude that (x + 1) is not a factor of x² + x³ + x + 1.