b. \(x^4+2x^3-7x^2-8x+12=0\)
\(\Leftrightarrow x^4-x^3+3x^3-3x^2-4x^2+4x-12x+12=0\)
\(\Leftrightarrow x^3\left(x-1\right)+3x^2\left(x-1\right)-4x\left(x-1\right)-12\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3+3x^2-4x-12\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^3-2x^2+5x^2-10x+6x-12\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x-2\right)+5x\left(x-2\right)+6\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x^2+5x+6\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x^2+2x+3x+6\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+2\right)\left(x+3\right)=0\)
\(\Leftrightarrow x=1\) hay \(x=2\) hay \(x=-2\) hay \(x=-3\)
-Vậy \(S=\left\{1;2;-2;-3\right\}\)
