\(\[\begin{align} & \left( {{x}_{1}},{{y}_{1}} \right)+\left( {{x}_{2}},{{y}_{2}} \right)=\left( {{x}_{1}}+{{x}_{2}},{{y}_{1}}+{{y}_{2}} \right) \\ & k\left( x,y \right)=\left( kx,ky \right) \\ & \left( {{x}_{1}},{{x}_{2}},\ldots ,{{x}_{n}} \right)+\left( {{y}_{1}},{{y}_{2}},\ldots ,{{y}_{n}} \right) \\ & \text{logo:} \\ & \left( {{x}_{1}}+{{y}_{1}},\ldots ,{{x}_{n}}+{{y}_{n}} \right) \\ & k.\left( {{x}_{1}},{{x}_{2}},\ldots ,{{x}_{n}} \right)\to \left( k{{x}_{1}},k{{x}_{2}},\ldots ,k{{x}_{n}} \right) \\ & Por\tan to \\ & p\left( x \right)\text{ }=\text{ }{{a}_{0}}+\text{ }{{a}_{1}}x\text{ }+\text{ }{{a}_{2}}x{}^\text{2}\text{ }+\ldots +\text{ }{{a}_{n}}{{x}^{n}} \\ & onde\text{ }{{a}_{i}}\to K\text{ }\left( i=0,1,2,\ldots ,n \right)\text{ } \\ & \text{ }\!\!\acute{\mathrm{E}}\!\!\text{ }um\text{ }espao\text{ }vetorial\text{ }sobre\text{ }o\text{ }corpo\text{ }K. \\ & \\ & \\ \end{align}\] \)