Editing Polynomial (section)

=== Positional notation ===
{{Main|Positional notation}}
In modern positional numbers systems, such as the [[Decimal|decimal system]], the digits and their positions in the representation of an integer, for example, 45, are a shorthand notation for a polynomial in the [[radix]] or base, in this case, {{nowrap|4 × 10<sup>1</sup> + 5 × 10<sup>0</sup>}}. As another example, in radix 5, a string of digits such as 132 denotes the (decimal) number {{nowrap|1 × 5<sup>2</sup> + 3 × 5<sup>1</sup> + 2 × 5<sup>0</sup>}} = 42. This representation is unique.  Let ''b'' be a positive integer greater than 1.  Then every positive integer ''a'' can be expressed uniquely in the form

<math display="block">a = r_m b^m + r_{m-1} b^{m-1} + \dotsb + r_1 b + r_0,</math>
where ''m'' is a nonnegative integer and the ''r'''s are integers such that

{{math|0 < ''r''<sub>''m''</sub> < ''b''}} and {{math|0 ≤ ''r''<sub>''i''</sub> < ''b''}} for {{math|1=''i'' = 0, 1, . . . , ''m'' − 1}}.<ref>{{harvnb|McCoy|1968|p=75}}</ref>