Đáp án + Giải thích các bước giải:

 `a, x^2 + 5x + 6=0`

`<=> x^2 + 2x + 3x + 6=0`

`<=> x(x+2)+3(x+2)=0`

`<=> (x+2)(x+3)=0`

`<=>` \(\left[ \begin{array}{l}x+2=0\\x+3=0\end{array} \right.\)

`<=>` \(\left[ \begin{array}{l}x=-2\\x=-3\end{array} \right.\) 

Vậy `x=-2;x=-3`

`b,x^2 - 10x + 16=0`

`<=> x^2 -8x-2x+16=0`

`<=> x(x-8)-2(x-8)=0`

`<=> (x-2)(x-8)=0`

`<=>` \(\left[ \begin{array}{l}x-2=0\\x-8=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=2\\x=8\end{array} \right.\) 

Vậy `x=2;x=8` 

`c, x^2 -10x+21=0`

`<=>x^2 -7x-3x+21=0`

`<=> x(x-7)-3(x-7)=0`

`<=> (x-3)(x-7)+0`

`<=>` \(\left[ \begin{array}{l}x-3=0\\x-7=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=3\\x=7\end{array} \right.\) 

Vậy `x=3;x=7`

`d, x^2 - 2x -3=0`

`<=>x^2 +x-3x-3=0`

`<=> x(x+1)-3(x+1)=0`

`<=> (x-3)(x+1)=0`

`<=>` \(\left[ \begin{array}{l}x-3=0\\x+1=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=3\\x=-1\end{array} \right.\) 

Vậy `x=3;x=-1`

`e, 2x^2 +7x+3=0`

`<=>2x^2 +6x+x+3=0`

`<=> 2x(x+3)+(x+3)=0`

`<=> (2x+1)(x+3)=0`

`<=>` \(\left[ \begin{array}{l}2x+1=0\\x+3=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=-1/2\\x=-3\end{array} \right.\) 

Vậy `x=-1/2 ; x=-3`

`d, x^2 -x - 6=0`

`<=> x^2 -3x+2x-6=0`

`<=> x(x-3)+2(x-3)=0`

`<=> (x+2)(x-3)=0`

`<=>` \(\left[ \begin{array}{l}x+2=0\\x-3=0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=-2\\x=3\end{array} \right.\) 

Vậy `x=-2;x=3`