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is-it-a-polynomial-2x-2-3x-2-x-2-




Question Number 206036 by Davidtim last updated on 05/Apr/24
is it a polynomial?  2x^2 +3x−(2/x^(−2) )
$${is}\:{it}\:{a}\:{polynomial}? \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\frac{\mathrm{2}}{{x}^{−\mathrm{2}} } \\ $$
Answered by Frix last updated on 05/Apr/24
(2/x^(−2) )=2x^2  ⇒2x^2 +3x−(2/x^(−2) )=3x  Which is a polynomial.
$$\frac{\mathrm{2}}{{x}^{−\mathrm{2}} }=\mathrm{2}{x}^{\mathrm{2}} \:\Rightarrow\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\frac{\mathrm{2}}{{x}^{−\mathrm{2}} }=\mathrm{3}{x} \\ $$$$\mathrm{Which}\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynomial}. \\ $$
Commented by A5T last updated on 05/Apr/24
If we were to consider it in the state before  simplication, then f(0) would not exist.  (2/x^(−2) )=2x^2  if x≠0
$${If}\:{we}\:{were}\:{to}\:{consider}\:{it}\:{in}\:{the}\:{state}\:{before} \\ $$$${simplication},\:{then}\:{f}\left(\mathrm{0}\right)\:{would}\:{not}\:{exist}. \\ $$$$\frac{\mathrm{2}}{{x}^{−\mathrm{2}} }=\mathrm{2}{x}^{\mathrm{2}} \:{if}\:{x}\neq\mathrm{0} \\ $$
Commented by Frix last updated on 05/Apr/24
You′re right.
$$\mathrm{You}'\mathrm{re}\:\mathrm{right}. \\ $$

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