\(x^3+6x^2-13x-42=0\)
\(\Leftrightarrow\left(x^3-3x^2\right)+\left(9x^2-27x\right)+\left(14x-42\right)=0\)
\(\Leftrightarrow x^2\left(x-3\right)+9x\left(x-3\right)+14\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)+\left(x^2+9x+14\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2+7x+2x+14\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left[x\left(x+7\right)+2\left(x+7\right)\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+2\right)\left(x+7\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-3=0\\x+2=0\\x+7=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=3\\x=-2\\x=-7\end{array}\right.\)
x3 + 6x2 - 13x - 42 = 0
=> x3 - 3x2 + 9x2 - 27x + 14x - 42 = 0
=> x2 ( x - 3 ) + 9x ( x - 3 ) + 14 ( x - 3 ) = 0
=> ( x - 3 ) ( x2 + 9x + 14) = 0
=> ( x - 3 ) ( x2 + 2x + 7x + 14 ) = 0
=> ( x - 3 ) [ x ( x + 2 ) + 7 ( x + 2 ) ] = 0
=> ( x - 3 ) ( x + 2 ) ( x + 7 ) = 0
=> x - 3 = 0 => x = 3
=> x + 2 = 0 => x = -2
=> x + 7 = 0 => x = -7
