Factor (mod 2) all eight polynomials of the form x3 + b2x2 + b1x + b0 into polynomials that are irreducible over F2, where bi ∈ {0, 1}. For example, x3 + x2 = x2(x + 1), now continue the other 7. Recall, the irreducible polynomials over F2 of degree 3 or less are x, x + 1, x2 + x + 1, x3 + x + 1, and x3 + x2 + 1.
Factor (mod 2) all eight polynomials of the form x3 + b2x2 + b1x + b0...
3. Factor (mod 2) all eight polynomials of the form 23 + b2x2 + b1x + bo into polynomials that are irreducible over F2, where bi E {0,1}. For example, x3+1 = (x+1)(x2+x+1), now you do the other 7. Recall, the irreducible polynomials over F2 of degree 3 or less are x, x + 1, x2 + x + 1, 2:3 + x + 1, and 2.3 + x2 +1.
A polynomial p(x) is an expression in variable x which is in the form axn + bxn-1 + …. + jx + k, where a, b, …, j, k are real numbers, and n is a non-negative integer. n is called the degree of polynomial. Every term in a polynomial consists of a coefficient and an exponent. For example, for the first term axn, a is the coefficient and n is the exponent. This assignment is about representing and computing...
79 Consider the function f(1) = -2(x + 1)3 Answer all parts: (a) - (f). (a) What is the degree of f(x)? The degree of f(s) is (b) Which of the following choices describe the end behavior of f(x)? The graph of f(x) acts Olike 72 (ie both ends up) o like - 22 (ie both ends down) O like x3 (ie, lett end down, right end up) Olike - (ie, left end up right end down) None of the...
Each of these problems (Problems 1-4) is worth four points Definition: Two lines or curves are said to be normal to each other at their point of intersection if they intersect there at right angles or, equivalently, if their tangent lines at the point of intersection are 1. A well-known theorem in geometry states that a line which is tangent to a circle is perpendicular to the radius of the circle at the point of tangency. Use implicit differentiation to...
Could you please answer the question Q1 to Q3. Write the answer
clearly and step by step.
1 Let U = {1, 2, 3, 4, 5, 6, 7} be the universe. Form the set A as follows: Read off your seven digit student number from left to right. For the first digit ni include the number 1 in A if ni is even otherwise omit 1 from A. Now take the second digit n2 and include the number 2 in...
Question 1 Not yet answered Marked out of 1.00 Flag question Solve the following pair of simultaneous equations. -3.- 5y = -13, 5x + 4y = 26. Give your answers exactly, as integers or single fractions. The solution is: x = y= Question 2 Not yet answered Marked out of 1.00 Flag question Suppose that the number of atoms of a particular isotope at time t (in hours) is given by the exponential decay function f(t) = -0.578. By what...
/***********************************
*
* Filename: poly.c
*
*
************************************/
#include "poly.h"
/*
Initialize all coefficients and exponents of the polynomial to zero.
*/
void init_polynom( int coeff[ ], int exp[ ] )
{
/* ADD YOUR CODE HERE */
} /* end init_polynom */
/*
Get inputs from user using scanf() and store them in the polynomial.
*/
void get_polynom( int coeff[ ], int exp[ ] )
{
/* ADD YOUR CODE HERE */
} /* end get_polynom */
/*
Convert...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...
I have to use the following theorems to determine whether or not
it is possible for the given orders to be simple.
Theorem 1: |G|=1 or prime, then it is simple.
Theorem 2: If |G| = (2 times an odd integer), the G is not
simple.
Theorem 3: n is an element of positive integers, n is not prime,
p is prime, and p|n.
If 1 is the only divisor of n that is congruent to 1 (mod p)
then...
This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this patternThese are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern x _________ x xx __________ x xx xxx __________ x xx xxx xxxx to see why they're called triangular numbers. I think the Pythagoreans (around 700 B.C.E.) were the ones who gave them this name. I do know the...