Given: Z [x] is the set of all polynomials with variable x and integer coefficients with the operations of polynomial addition and multiplication. A general element in Z [x] has the form
ƒ(x) = an x n + an-1 x n-1 + … + a1 x + a0
where an , an-1, …, a1, a0 are integers and n is a non-negative integer.
Z [x] is a ring but not a field.
1. Choose a specific polynomial in Z [x], and prove that no other polynomial in Z [x] is its multiplicative inverse. Justify your work.
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