01204211/activity8 polynomials and graph theory 1

This is part of 01204211-58.

In-class activities

Polynomials

To work on these questions, you can refer to this lecture note from Berkeley.

For this set of activities, we shall work modulo 11.

We will use your student ID as a data. For $i=0,...,9$, let $a_{i}$ denote the $i$-th digit (counting from the lest, starting at 0) of your student ID. For example if your student ID is 5755543210, $a_{0}=0$, $a_{2}=2$, $a_{9}=5$, $a_{8}=7$

A.1-1 We shall use your last 4 digits: $a_{0},a_{1},a_{2},a_{3}$. Find a polynomial $f$ of degree 3 such that $f(x)=a_{x}$ for $i=0,\ldots ,3$. You should start by write down $\Delta _{i}(x)$.