what is x^2 + 2x +1 divided by x-1 ?

Answer 1

Using synthetic division:

1 | 1 2 1

1 3

1 3 4

This translates to:

x + 1 + 4/(x-1)

Answer 2

You would use long division or synthetic division here.

x² + 2x + 1 = (x² - x) + (3x - 3) + 4 = x(x - 1) + 3(x - 1) + 4 = (x+3)(x-1) + 4

Therefore (x² + 2x + 1) / ( x - 1) = [ (x+3)(x-1) + 4 ] / (x - 1) = x + 3 + 4/(x-1)

Answer 3

x+3 with remainder of 4

or

x+3 + 4/(x-1)