How many polynomials are there&nbsp;b) of degree ≤ 2 in Z5[x]? (Include 0

A polynomial of degree&nbsp;≤2&nbsp;in Z5[x] has the form&nbsp;a0&nbsp;+a1x+a2x2, where the&nbsp;ai&nbsp;∈&nbsp;Z5. Note that any or all of the ai can be zero: if&nbsp;a2&nbsp;=&nbsp;0, we have a polynomial of degree&nbsp;&lt;&nbsp;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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2022-05-08

How many polynomials are there
b) of degree ≤ 2 in Z5[x]? (Include 0

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karton

Expert2022-07-25Added 613 answers

A polynomial of degree $\leq 2$ in Z5[x] has the form $a_{0} + a_{1} x + a_{2} x 2$ , where the $a i \in Z 5$ . 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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