a) \(\Rightarrow x^2-x-20=0\)
\(\Rightarrow\left(x-5\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
b) \(\Rightarrow x^2-x-6=0\)
\(\Rightarrow\left(x-3\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
c) \(\Rightarrow x^3+x^2+18=0\)
\(\Rightarrow x^2\left(x+3\right)-2x\left(x+3\right)+6\left(x+3\right)=0\)
\(\Rightarrow\left(x+3\right)\left(x^2-2x+6\right)=0\)
\(\Rightarrow x=-3\left(do.x^2-2x+6=\left(x-1\right)^2+5\ge5>0\right)\)
d) \(\Rightarrow x^3\left(x-1\right)+4x^2\left(x-1\right)+4x\left(x-1\right)+3\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^3+4x^2+4x+3\right)=0\)
\(\Rightarrow\left(x-1\right)\left[x^2\left(x+3\right)+x\left(x+3\right)+\left(x+3\right)\right]=0\)
\(\Rightarrow\left(x-1\right)\left(x+3\right)\left(x^2+x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)(do \(x^2+x+1=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0\))
