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Ife is any homomorphism of the type in 40.5, then Kere = (b(x))for some b(x) E F[x]

Chapter 40, Problem 40.6

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QUESTION:

Ife is any homomorphism of the type in 40.5, then Kere = (b(x))for some b(x) E F[x], byTheorem 40.3. Determine such a polynomial b(x) for each of the following examples. (Suggestion:Use the Factor Theorem.) e: iQ[x] -+ iQ by e(f(x = f(O)

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QUESTION:

Ife is any homomorphism of the type in 40.5, then Kere = (b(x))for some b(x) E F[x], byTheorem 40.3. Determine such a polynomial b(x) for each of the following examples. (Suggestion:Use the Factor Theorem.) e: iQ[x] -+ iQ by e(f(x = f(O)

ANSWER:

Step 1 of 3

Factor Theorem: For  if and only if  is a factor of .

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