Question

Find the quotient following this pattern

image attached

Answer 1

x ^5 + x ^4 + x ^3 + x ^2 + x + 1

Answer 2

The answer to your question is below

Explanation:

`(x^(6)- 1 )/(x -1) = (x^(6)+ 0x^(5) + 0x^(4) + 0x^(3) + 0x^(2) + 0x - 1 )/(x - 1)`

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