вправа 739 гдз 7 клас алгебра Мерзляк Полонський
7 клас ➠ алгебра ➠ Мерзляк Полонський
Вправа 739
Відповідь:
\begin{equation}1)x^{4}-5x^{2}+4=\end{equation}
\begin{equation}=x^{4}-x^{2}-4x^{2}+4=\end{equation}
\begin{equation}=x^{2}\left ( x^{2}-1 \right )-4\left ( x^{2}-1 \right )=\end{equation}
\begin{equation}=\left ( x^{2}-1 \right )\left ( x^{2}-4 \right )=\end{equation}
\begin{equation}=\left ( x-1 \right )\left ( x+1 \right )\left ( x-2 \right )\left ( x+2 \right );\end{equation}
\begin{equation}2)x^{4}+x^{2}+1=\end{equation}
\begin{equation}=x^{4}+2x^{2}+1-x^{2}=\end{equation}
\begin{equation}=\left ( x^{2}+1 \right )^{2}-x^{2}=\end{equation}
\begin{equation}=\left ( x^{2}+1-x \right )\left ( x^{2}+1+x \right )=\end{equation}
\begin{equation}=\left ( x^{2}-x+1 \right )\left ( x^{2}+x+1 \right );\end{equation}
\begin{equation}3)4x^{4}-12x^{2}+1=\end{equation}
\begin{equation}=\left ( 4x^{4}+4x^{2}+1 \right )-16x^{2}=\end{equation}
\begin{equation}=\left ( 2x^{2}+1 \right )^{2}-\left ( 4x \right )^{2}=\end{equation}
\begin{equation}=\left ( 2x^{2}+1-4x \right )\left ( 2x^{2}+1+4x \right )=\end{equation}
\begin{equation}=\left ( 2x^{2}-4x+1 \right )\left ( 2x^{2}+4x+1 \right );\end{equation}
\begin{equation}4)x^{5}+x+1=\end{equation}
\begin{equation}=x^{5}-x^{2}+x^{2}+x+1=\end{equation}
\begin{equation}=x^{2}\left ( x^{3}-1 \right )+\left ( x^{2}+x+1 \right )=\end{equation}
\begin{equation}=x^{2}\left ( x-1 \right )\left ( x^{2}+x+1 \right )+\end{equation}
\begin{equation}+\left ( x^{2}+x+1 \right )=\end{equation}
\begin{equation}=\left ( x^{2}+x+1 \right )\left ( x^{2}\left ( x-1 \right )+1 \right )=\end{equation}
\begin{equation}=\left ( x^{2}+x+1 \right )\left ( x^{3}-x^{2}+1 \right );\end{equation}
\begin{equation}5)x^{4}+4=\end{equation}
\begin{equation}=x^{4}+4x^{2}+4-4x^{2}=\end{equation}
\begin{equation}=\left ( x^{2}+2 \right )^{2}-\left ( 2x \right )^{2}=\end{equation}
\begin{equation}=\left ( x^{2}+2-2x \right )\left ( x^{2}+2+2x \right )=\end{equation}
\begin{equation}=\left ( x^{2}-2x+2 \right )\left ( x^{2}+2x+2 \right );\end{equation}
\begin{equation}6)x^{8}+x^{4}-2=\end{equation}
\begin{equation}=x^{8}-1+x^{4}-1=\end{equation}
\begin{equation}=\left ( x^{4}-1 \right )\left ( x^{4}+1 \right )+\left ( x^{4}-1 \right )=\end{equation}
\begin{equation}=\left ( x^{4}-1 \right )\left ( x^{4}+2 \right )=\end{equation}
\begin{equation}=\left ( x^{2}-1 \right )\left ( x^{2}+1 \right )\left ( x^{4}+2 \right )=\end{equation}
\begin{equation}=\left ( x-1 \right )\left ( x+1 \right )\left ( x^{2}+1 \right )\left ( x^{4}+2 \right ).\end{equation}