a: \(x^2+5x+6=0\)
=>(x+2)(x+3)=0
=>\(\left[{}\begin{matrix}x+2=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-3\end{matrix}\right.\)
b: \(x^2-7x+12=0\)
=>\(x^2-3x-4x+12=0\)
=>x(x-3)-4(x-3)=0
=>(x-3)(x-4)=0
=>\(\left[{}\begin{matrix}x-3=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
c: \(2x^2-9x+10=0\)
=>\(2x^2-4x-5x+10=0\)
=>2x(x-2)-5(x-2)=0
=>(x-2)(2x-5)=0
=>\(\left[{}\begin{matrix}x-2=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{5}{2}\end{matrix}\right.\)
d: \(-x^2+4x+5=0\)
=>\(x^2-4x-5=0\)
=>(x-5)(x+1)=0
=>\(\left[{}\begin{matrix}x-5=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)
e: \(x^3-5x^2+2x+8=0\)
=>\(x^3+x^2-6x^2-6x+8x+8=0\)
=>\(x^2\left(x+1\right)-6x\left(x+1\right)+8\left(x+1\right)=0\)
=>\(\left(x+1\right)\left(x^2-6x+8\right)=0\)
=>(x+1)(x-2)(x-4)=0
=>\(\left[{}\begin{matrix}x+1=0\\x-2=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\\x=4\end{matrix}\right.\)
f: \(x^3+2x^2-13x+10=0\)
=>\(x^3+5x^2-3x^2-15x+2x+10=0\)
=>\(x^2\left(x+5\right)-3x\left(x+5\right)+2\left(x+5\right)=0\)
=>\(\left(x+5\right)\left(x^2-3x+2\right)=0\)
=>(x+5)(x-1)(x-2)=0
=>\(\left[{}\begin{matrix}x+5=0\\x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=1\\x=2\end{matrix}\right.\)
