5.4E: Divisão de polinômios (exercícios)
- Page ID
- 187144
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
Para os exercícios a seguir, use a divisão longa para encontrar o quociente e o restante.
19. \(\frac{x^{3}-2 x^{2}+4 x+4}{x-2}\)
20. \(\frac{3 x^{4}-4 x^{2}+4 x+8}{x+1}\)
Para os exercícios a seguir, use a divisão sintética para encontrar o quociente. Se o divisor for um fator, escreva a forma fatorada.
21. \(\frac{x^{3}-2 x^{2}+5 x-1}{x+3}\)
22. \(\frac{x^{3}+4 x+10}{x-3}\)
23. \(\frac{2 x^{3}+6 x^{2}-11 x-12}{x+4}\)
24. \(\frac{3 x^{4}+3 x^{3}+2 x+2}{x+1}\)