Question 443181
t-1 |  t^3 -t^2 +t -1

How many times does t go into t^3? t^2
(t-1)t^2 = t^3 - t^2

t^3 - t^2 + t -1
-(t^3 - t^2)
=================
0 + t -1
========
How many times does t go into t-1? 1
t-1
-(t-1)
======
0
=======
Remainder of 0, then t-1 divides evenly, and you get t^2 + 1. 

Let's check this.

(t-1)(t^2+1) ------by foil ----->t^3 - t^2 +t -1 
So yes, we're right.