Consider the quotient ring R = Q[x] x² − 4 > (a) Give an example of a zero divisor in R. Explain why it is a zero divisor. (b) Find -1 (x+ < x² − 4 >)¯¹in R (you should be able to see this without solving) = (c) Find (3+x)−¹ = (3+ < x² − 4 >)−¹(you can find it by solving, as - we did in class)

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A: The solution is given as follows

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Q: Give the smallest extension of Q that contains all the zeros of (x4 – 8x² + 15)(x² + 1). -

A: Yes