find the quotient following this pattern
image attached

Answer:
The answer to your question is below
Step-by-step explanation:
[tex]\frac{x^{6}- 1 }{x -1} = \frac{x^{6}+ 0x^{5} + 0x^{4} + 0x^{3} + 0x^{2} + 0x - 1 }{x - 1}[/tex]
Synthetic division
1 0 0 0 0 0 -1 1
1 1 1 1 1 1
1 1 1 1 1 1 0
Quotioent = x⁵ + x⁴ + x³ + x² + x
Remainder = 0