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

DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?

Building Envelope The building code in a certain town requires that a house be at least 10 ft from the boundaries of the lot. The buildable area or building envelope for the rectangular lot shown in the following figure is given by A=(x20)(y20) a Explain how the expression for A is obtained. b Expand to express A as a polynomial in x and y. c A contractor has a choice of purchasing one of two rectangular lots, each having the same area. One lot measures 100 ft by 400 ft; the other measures 200 ft by 200 ft. Which lot has the larger building envelope?

11. a. List all the polynomials in that have degree 2. b. Determine which of the polynomials in part a are units. If none exists, state so.