2022-05-08

How many polynomials are there

b) of degree ≤ 2 in Z5[x]? (Include 0

karton

Expert2022-07-25Added 613 answers

A polynomial of degree $\le 2$ in Z5[x] has the form ${a}_{0}+{a}_{1}x+{a}_{2}x2$, where the $ai\in Z5$. Note that any or all of the ai can be zero: if ${a}_{2}=0$, we have a polynomial of degree $<2$, if all are 0, we have the zero polynomial. There are 5 choices for each ai, so there are 53 = 125 such polynomials.

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