16. Sabendo que A e B são dois polinômios, se A - B = 0, então: (
A) (A + B) - B = 0.
(B) (A-B) - B=0.
(C) A - B = A + (-B) = 0.
(D) -A + (-B) = 0.
(E) -A- (+B) = 0.
A) (A + B) - B = 0.
(B) (A-B) - B=0.
(C) A - B = A + (-B) = 0.
(D) -A + (-B) = 0.
(E) -A- (+B) = 0.
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✅ Verificando as identidades polinomiais:
Se A e B são dois polinômios, tais que:
[tex]\Large\displaystyle\text{$\begin{gathered} A - B = 0\end{gathered}$}[/tex]
Então, isso implica que:
[tex]\Large\displaystyle\text{$\begin{gathered} A = B\:\:\:\textrm{com}\:\:A\neq0\:\:e\:\:B\neq0\end{gathered}$}[/tex]
Desse modo devemos verificar se as seguintes respostas são verdadeiras:
[tex]\Large\displaystyle\text{$\begin{gathered} (A + B) - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A + B - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Se}\:\:A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} B = 0\end{gathered}$}[/tex]
Portanto é:
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Falso}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} (A - B) - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A - B - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A - 2B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Se}\:\:A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A - 2A = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A = 0\end{gathered}$}[/tex]
Portanto é:
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Falso}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A - B = A + (-B) = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A - B = A - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Se}\:\:A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} A - A = A - A = 0\end{gathered}$}[/tex]
Portanto:
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Positivo}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A + (-B) = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Se}\:\:A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A = A\end{gathered}$}[/tex]
Portanto:
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Falso}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A - (+B) = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A - B = 0\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Se}\:\:A = B\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -A = A\end{gathered}$}[/tex]
Portanto:
[tex]\Large\displaystyle\text{$\begin{gathered} \textrm{Falso}\end{gathered}$}[/tex]
[tex]\LARGE\displaystyle\text{$\begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered}$}[/tex]
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