回復 19# 阿光 的帖子
填充第7題
\(\begin{align}
& 2{{x}^{6}}-3{{x}^{5}}+4{{x}^{4}}-3{{x}^{3}}+4{{x}^{2}}-3x+2 \\
& =\left( 2{{x}^{6}}+4{{x}^{4}}+4{{x}^{2}}+2 \right)-\left( 3{{x}^{5}}+3{{x}^{3}}+3x \right) \\
& =2\left( {{x}^{6}}+{{x}^{4}}+{{x}^{2}}+{{x}^{4}}+{{x}^{2}}+1 \right)-3x\left( {{x}^{4}}+{{x}^{2}}+1 \right) \\
& =2\left( {{x}^{4}}+{{x}^{2}}+1 \right)\left( {{x}^{2}}+1 \right)-3x\left( {{x}^{4}}+{{x}^{2}}+1 \right) \\
& =\left( {{x}^{4}}+{{x}^{2}}+1 \right)\left( 2{{x}^{2}}-3x+2 \right) \\
& =\left( {{x}^{2}}-x+1 \right)\left( {{x}^{2}}+x+1 \right)\left( 2{{x}^{2}}-3x+2 \right) \\
\end{align}\)