The answer to “Let f (x) be a nonconstant element of F[x]. If a belongs to some extension of F and f (a) is algebraic over F, prove that a is algebraic over F.” is broken down into a number of easy to follow steps, and 31 words. This textbook survival guide was created for the textbook: Contemporary Abstract Algebra , edition: 8th. Contemporary Abstract Algebra was written by and is associated to the ISBN: 9781133599708. The full step-by-step solution to problem: 22E from chapter: 21 was answered by , our top Math solution expert on 07/25/17, 05:55AM. This full solution covers the following key subjects: Algebraic, let, element, extension, belongs. This expansive textbook survival guide covers 34 chapters, and 2038 solutions. Since the solution to 22E from 21 chapter was answered, more than 220 students have viewed the full step-by-step answer.