The example in the previous question used polynomials whose coefficients were in the set {0, 1,2,3,4,5,6,7,8,9}. Now consider the case were coefficients are drawn from {0, 1, 2, 3, ...m - 1} where m is a Natural number and m > 2. In order words the set of polynomials in Zm[X]. Consider the special case m = 2 of binary values. - = 1. How might one write the binary value 1001010 as a degree six polynomial, p(x) in Z2[X]? 2. Similarly how might one write the octal value (base 8) 6723 as a degree three polynomial, q(x) in Z8[X]? 3. The octal value 6723 corresponds to the binary value 0110011100100011. What does this indicate about expressing the octal value 672 as a polynomial in Z2[X]? What would the degree of this polynomial be? 4. A number of large-scale applications involve numerical quantities requiring several thousands of binary digits in representing values (for example cryptographic schemes, data from some some scientific experiments), In such cases it is not realistic to carry out arithmetic as a basic computer operation since this will be limited by the word size of the machine (currently this will rarely exceed 128 bits). What is the only option for performing arithmetic involving numbers with many thousands of bits? If the "standard school methods" are used why might these be problematic? 5. Given the connection between number representation in some base m and polynomials in Zm[X] what does this suggest as an alternative approach to carrying out multiplication of very large numerical quantities