Regra de Ruffini e divisão polinomial longa (notação inglesa)

Regra de Rufini de  (x^5-1024)/(x-4)

\begin{array}{c|rrrrrl}&x^{5}&x^{4}&x^{3}&x^{2}&x^{1}&\phantom{-}x^{0}\\&1&0&0&0&0&-1024\\4&\downarrow&4&16&64&256&\phantom{-}1024\\\hline&1&4&16&64&256&\phantom{-102}0=\text{resto}\\&x^{4}&x^{3}&x^{2}&x^{1}&x^{0}\end{array}

Divisão polinomial longa (notação inglesa) de (x^5-1024)/(x-4)

\begin{array}{rl}&\underline{\phantom{+x^{5}}\phantom{+0}x^{4}\phantom{0}+4x^{3}+16x^{2}\phantom{0}+64x\phantom{0}+256\phantom{0}}\\x-4)& \phantom{+}x^{5}\phantom{+0x^{4}0+4x^{3}+16x^{2}+064x}-1024\\&\underline{-x^{5}+4x^4\phantom{0}}\\&\phantom{-x^{5}+}\;4x^4\\ &\phantom{-x^{5}}\underline{\;-4x^4+16x^3\phantom{0}}\\&\phantom{-x^{5}-4x^4+}16x^3\\ &\phantom{-x^{5}-4x^4}\underline{\;-16x^3+64x^{2}\phantom{0}}\\&\phantom{-x^{5}-4x^4+16x^3+}64x^{2}\\&\phantom{-x^{5}-4x^4+16x^3}\underline{\;-64x^{2}+256x\phantom{0}}\\&\phantom{-x^{5}-4x^4+16x^3-64x^{2}+}256x-1024\\&\phantom{-x^{5}-4x^4+16x^3-64x^{2}}\underline{\;-256x+1024\phantom{0}}\\&\phantom{-x^{5}-4x^4+16x^3-64x^{2}-256x+102}0\end{array}

Anúncios
Regra de Ruffini e divisão polinomial longa (notação inglesa)

Tabelas

Tabelas e respectivos códigos LaTeX (falta “latex” a seguir ao 1.º $)

 

\begin{array}{llccc}\hline\text{Medalha}& &\text{Categoria J\'unior}&\text{Categoria A}&\text{Categoria B}\\\hline \text{Ouro}&\text{rapazes - raparigas}&3 - 0 & 2 - 1 & 3 - 0\\ \text{Prata}&\text{rapazes - raparigas}& 3 - 0 & 3 - 0 & 3 - 0 \\\text{Bronze} &\text{rapazes - raparigas}& 4 - 2 & 5 - 1 & 6 - 0\\\hline\end{array}

 

$\begin{array}{llccc}\hline\text{Medalha}& &\text{Categoria J\’unior}&\text{Categoria A}&\text{Categoria B}\\\hline \text{Ouro}&\text{rapazes – raparigas}&3 – 0 & 2 – 1 & 3 – 0\\ \text{Prata}&\text{rapazes – raparigas}& 3 – 0 & 3 – 0 & 3 – 0 \\\text{Bronze} &\text{rapazes – raparigas}& 4 – 2 & 5 – 1 & 6 – 0\\\hline\end{array}&bg=ffffff&fg=0000ff$

 

\begin{array}{llccc}\hline\text{Medalha}& &\text{Categoria J\'unior}&\text{Categoria A}&\text{Categoria B}\\\hline \text{Ouro}&\text{rapazes - raparigas}&3 - 0 & 2 - 1 & 3 - 0\\ \text{Prata}&\text{rapazes - raparigas}& 3 - 0 & 3 - 0 & 3 - 0 \\\text{Bronze} &\text{rapazes - raparigas}& 4 - 2 & 5 - 1 & 6 - 0\\\hline\end{array}

 

$\begin{array}{llccc}\hline\text{Medalha}& &\text{Categoria J\’unior}&\text{Categoria A}&\text{Categoria B}\\\hline \text{Ouro}&\text{rapazes – raparigas}&3 – 0 & 2 – 1 & 3 – 0\\ \text{Prata}&\text{rapazes – raparigas}& 3 – 0 & 3 – 0 & 3 – 0 \\\text{Bronze} &\text{rapazes – raparigas}& 4 – 2 & 5 – 1 & 6 – 0\\\hline\end{array}&fg=000000$

 

\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\'unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{rapazes - raparigas}&3 - 0 & 2 - 1 & 3 - 0\\ \text{Prata}&\text{rapazes - raparigas}& 3 - 0 & 3 - 0 & 3 - 0 \\\text{Bronze} &\text{rapazes - raparigas}& 4 - 2 & 5 - 1 & 6 - 0\\\hline\end{array}

 

$\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\’unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{rapazes – raparigas}&3 – 0 & 2 – 1 & 3 – 0\\ \text{Prata}&\text{rapazes – raparigas}& 3 – 0 & 3 – 0 & 3 – 0 \\\text{Bronze} &\text{rapazes – raparigas}& 4 – 2 & 5 – 1 & 6 – 0\\\hline\end{array}&fg=000000$

 

 

\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\'unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{\small {rapazes - raparigas}}&3 - 0 & 2 - 1 & 3 - 0\\ \text{Prata}&\text{\small {rapazes - raparigas}}& 3 - 0 & 3 - 0 & 3 - 0 \\\text{Bronze} &\text{\small {rapazes - raparigas}}& 4 - 2 & 5 - 1 & 6 - 0\\\hline\end{array}

 

$\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\’unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{\small {rapazes – raparigas}}&3 – 0 & 2 – 1 & 3 – 0\\ \text{Prata}&\text{\small {rapazes – raparigas}}& 3 – 0 & 3 – 0 & 3 – 0 \\\text{Bronze} &\text{\small {rapazes – raparigas}}& 4 – 2 & 5 – 1 & 6 – 0\\\hline\end{array}&bg=ffffff&fg=0000ff$

 

———–

\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\'unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{rapazes - raparigas}&3 - 0 & 2 - 1 & 3 - 0\\ \text{Prata}&\text{rapazes - raparigas}& 3 - 0 & 3 - 0 & 3 - 0 \\\text{Bronze} &\text{rapazes - raparigas}& 4 - 2 & 5 - 1 & 6 - 0\\\hline\end{array}

 

$\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\’unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{rapazes – raparigas}&3 – 0 & 2 – 1 & 3 – 0\\ \text{Prata}&\text{rapazes – raparigas}& 3 – 0 & 3 – 0 & 3 – 0 \\\text{Bronze} &\text{rapazes – raparigas}& 4 – 2 & 5 – 1 & 6 – 0\\\hline\end{array}&fg=000000$

 

\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\'unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{\small {rapazes - raparigas}}&3 - 0 & 2 - 1 & 3 - 0\\ \text{Prata}&\text{\small {rapazes - raparigas}}& 3 - 0 & 3 - 0 & 3 - 0 \\\text{Bronze} &\text{\small {rapazes - raparigas}}& 4 - 2 & 5 - 1 & 6 - 0\\\hline\end{array}

 

$\begin{array}{llccc}\hline\text{Medalha}& &\text{Cat. J\’unior}&\text{Cat. A}&\text{Cat. B}\\\hline \text{Ouro}&\text{\small {rapazes – raparigas}}&3 – 0 & 2 – 1 & 3 – 0\\ \text{Prata}&\text{\small {rapazes – raparigas}}& 3 – 0 & 3 – 0 & 3 – 0 \\\text{Bronze} &\text{\small {rapazes – raparigas}}& 4 – 2 & 5 – 1 & 6 – 0\\\hline\end{array}&fg=000000$

 

Tabelas