1. Let F2 = {0, 1} be the field with two elements, and let Fg consist...

 

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1. Let F2 = {0, 1} be the field with two elements, and let Fg consist of the expressions a + bæ + cz2. where a, b, c are elements of F, and x is a symbol such that = x + 1. With operations inherited from polynomials in one variable, show that the above is a field. 2. In a similar way, show that expressions of the form a + bx, with a, b e F, and a such that x? = 2, form the field F, with 9 elements. 1. Let F2 = {0, 1} be the field with two elements, and let Fg consist of the expressions a + bæ + cz2. where a, b, c are elements of F, and x is a symbol such that = x + 1. With operations inherited from polynomials in one variable, show that the above is a field. 2. In a similar way, show that expressions of the form a + bx, with a, b e F, and a such that x? = 2, form the field F, with 9 elements.