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Show that x3 + x2 + x + 1 is reducible over Q. Does this
Chapter 17, Problem 11E(choose chapter or problem)
QUESTION:
Show that x3 + x2 + x + 1 is reducible over Q. Does this fact contradict the corollary to Theorem 17.4?Reference:
Questions & Answers
QUESTION:
Show that x3 + x2 + x + 1 is reducible over Q. Does this fact contradict the corollary to Theorem 17.4?Reference:
ANSWER:Step 1 of 3
Consider the function
Need to show that f(x) is reducible over Q.
Recall the corollary, the factor theorem,
Let F be a field. And. Then a is a zero of f(x) if and only if is a factor of f(x)
Here,
Since is a zero of f(x), from the above corollary, is a factor of f(x).