The remainder when x^(2011) is divided by x^2 -3x+2 is ?
2 Answers
Explanation:
A semi-easy way to see this is to start dividing the expression using Long Division. Write the dividend (under the division symbol) with zeros as
We won't need all of the terms in order to notice the pattern.
As you start dividing, you will observe that the first term has a coefficient of 1, the second has a coefficient of 3, the third has a coefficient of 7, then 15, then 31, etc..
These numbers have the form
The remainder will appear after you have divided through the whole thing, consisting of the
The first term in the quotient will follow the same pattern, having
The same pattern is true for every division of the form
You may also notice that
See below.
Explanation:
where
Now we know
Solving for