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Please answer the following:
Let f(x) = x^p - alpha E F [x] be irreducible, and let alpha be a root of f in an extension field. Show that if F (alpha)/F is a Galois extension, then g(x) = x^p - 1 splits in the field F.
Solve the following exponential equation
Calculate the LCM
Making the graph of two polynomial functions.
Simplify the inequality
Solve the following equation for x.
Consider the set of polynomials with real coefficients. Define two elements of this set to be related if their derivatives are equal. Prove that this defines an equivalence relation.
Find the median, mean, mode & midrange
Make a graph and find the intervals.
Make a matrix to display the information
Using mod system
Calculate the length and width.
Find the maximum height
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