onsider a cyclic code C in R(2, 15) with the generator polynomial g(x) = 1 + x +x2 + x4 + x8. (Its distance is 5.) (a) Find the dimension of C.(b) Word w = 100000011101101 is received, assuming no more than 2 errors occur,find the error and repair it

onsider a cyclic code C in R(2, 15) with the generator polynomial g(x) = 1 + x +x2 + x4 + x8. (Its distance is 5.) (a) Find the dimension of C.(b) Word w = 100000011101101 is received, assuming no more than 2 errors occur,find the error and repair it

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given three polynomials over 2₂. find (i) (ii) f(x) + g(x). f(x)h(x). f(x) = 6x³-5x² + 2x - 4, g(x) = 5x³ + 2x² + 6x-1, h(x) = 3x² - 2x-5.
3x²-27 Eric was asked to evaluate ²+7+12 x²-4x+3 ÷ when x 0, x = -5, and x = 2. To avoid having to evaluate four quadratic polynomials multiple times, Eric decided to simplify the expression before evaluating it for the first value of x. His work is shown below in blue. 3x-27 X-4213 3x²-27 = х+7х на x²+7x112 x²-4x+3 3(x²-4) (x+4x(x+1) (x+4)(x+3) (-1)(x+4) =3(x+3)(x-3)(x+4)(x+1) (x+4)(x+3)(x-x+4) =3(x-3)(x+1) (x+4)(x-1) Now substitute O for x in the simplified expression 3(x-3)XXN) (x+4)(x-1) 360-50+1) 3(-3x1)- - (0++)(0-1) Question 8 (2 points) Listen ་ 4(-D a. Evaluate the original expression for x = 0. Be sure to show all of your steps. Paragraph B I U~ A Lato Recom 19p... T Add a Fe Record Video 4 هی 20
Explain the determine blue
could you please show how u found the correct answer as well as showing each step for the problem.
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3x²-27 Eric was asked to evaluate ²+7+12 x²-4x+3 ÷ when x 0, x = -5, and x = 2. To avoid having to evaluate four quadratic polynomials multiple times, Eric decided to simplify the expression before evaluating it for the first value of x. His work is shown below in blue. 3x-27 X-4213 3x²-27 = х+7х на x²+7x112 x²-4x+3 3(x²-4) (x+4x(x+1) (x+4)(x+3) (-1)(x+4) =3(x+3)(x-3)(x+4)(x+1) (x+4)(x+3)(x-x+4) =3(x-3)(x+1) (x+4)(x-1) Now substitute O for x in the simplified expression 3(x-3)XXN) (x+4)(x-1) 360-50+1) 3(-3x1)- - (0++)(0-1) Question 8 (2 points) Listen ་ 4(-D a. Evaluate the original expression for x = 0. Be sure to show all of your steps. Paragraph B I U~ A Lato Recom 19p... T Add a Fe Record Video 4 هی 20
59697/variants/954782/take/3/ When the following polynomial is written in standard form, identify each characteristic of the polynomial. 6x² + 4x + 5x³+2 Leading Coefficient Degree Constant Number of terms 0 0 0 0 0 0 0 0 0 0 0 ......000000 1 of 12 Total Questions Answered © 2 b. 4 5 d. 3 All Changes Saved V 11:20 PM 2/14/2023
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I Sakai : MATH 101 1 S1-2021: Re O https://sakaiug.edu.gh/access/o x /sakai.ug.edu.gh/access/content/group/MATH-101-1-S1-2021/Videos/Polynomial%20and%20Rational%20Functio olynomial%20f. Practice Exercise • Consider the polynomial P(x)= x³ – 4x² +ax – 3. Find a if, when P(x) is divided by r + 1, the remainder is –12. • Find the quadratic which has a remainder of 6 when divided by (x – 1), a remainder of 4 when divided by (x – 3) and no remainder when divided by (x + 1). • Consider the polynomial h(x) = 3.x* – kx2 – 6x + 8. Given that (x – 4) is a factor of h(x), Find k and find the other factors of h(x) 355 PM prt sc delete home num + backspace lock 96 8 9.