Đây nè bạn.

a, \(x^2-6=x^2-\sqrt{6^2}=\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)

b, \(x^2+2\sqrt{3}x+3=x^2+2\sqrt{3}x+\sqrt{3}=\left(x+\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)\left(x+\sqrt{3}\right)\)

c, \(x^2-2\sqrt{5}x+5=x^2-2\sqrt{5}x+\sqrt{5}=\left(x-\sqrt{5}\right)^2=\left(x-\sqrt{5}\right)\left(x-\sqrt{5}\right)\)

a: \(x^2-6=\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)

b: \(x^2+2\sqrt{3}x+3=\left(x+\sqrt{3}\right)^2\)

c: \(x^2-2\sqrt{5}x+5=\left(x-\sqrt{5}\right)^2\)

`-x^2 +7x-6`

`=-x^2 +6x+x-6`

`=x(6-x)-(6-x)`

`=(x-1)(6-x)`

=-(x^2-7x+6)

=-(x-1)(x-6)

\(=\left(6x^2-3x\right)+\left(4x-2\right)\)

\(=3x\left(2x-1\right)+2\left(2x-1\right)\)

\(=\left(3x+2\right)\left(2x-1\right)\)

\(=6x^2-3x+4x-2=6x\left(x-2\right)+2\left(x-2\right)=2\left(3x+2\right)\left(x-2\right)\)

a: \(P=x^2-5x+6\)

\(=x^2-2x-3x+6\)

\(=x\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right)\left(x-3\right)\)

b: \(P=3x^2+14x-5\)

\(=3x^2+15x-x-5\)

\(=3x\left(x+5\right)-\left(x+5\right)\)

\(=\left(x+5\right)\left(3x-1\right)\)

c: \(P=-2x^2-7x-5\)

\(=-\left(2x^2+7x+5\right)\)

\(=-\left(2x^2+2x+5x+5\right)\)

\(=-\left[2x\left(x+1\right)+5\left(x+1\right)\right]\)

\(=-\left(x+1\right)\left(2x+5\right)\)

Kiểm tra lại \(x^2-2y+y^2...\) hay \(x^2-2xy+y^2...\)

\(a^3+a+30\)

\(=a^3+3a^2-3a^2-9a+10a+30\)

\(=\left(a+3\right)\left(a^2-3a+10\right)\)

\(x^3+x^2+100\)

\(=x^3+5x^2-4x^2-20x+20x+100\)

\(=\left(x+5\right)\left(x^2-4x+20\right)\)

`a^3 + a - 30`

`= a^3 + 3a^2 - 3a^2 - 9a + 10a + 30`

`= (a + 3)(a^2 - 3a + 10)`

`--------------------`

`x^3 + x^2 + 100`

`= x^3 + 5x^2 - 4x^2 - 20x + 20x +100`

`= (x+5)(x^3 - 4x + 20)`

Lời giải:
a.

$7-3a=(\sqrt{7}-\sqrt{3a})(\sqrt{7}+\sqrt{3a})$

b. 

$14x^2-11=(\sqrt{14}x-\sqrt{11})(\sqrt{14}x+\sqrt{11})$

c.

$3x-6\sqrt{x}-6=3(x-2\sqrt{x}-2)$
$=3[(\sqrt{x}-1)^2-3]$

$=3(\sqrt{x}-1-\sqrt{3})(\sqrt{x}-1+\sqrt{3})$

d.

$x\sqrt{x}-3\sqrt{x}-2=x\sqrt{x}-2x+2x-4\sqrt{x}+\sqrt{x}-2$
$=x(\sqrt{x}-2)+2\sqrt{x}(\sqrt{x}-2)+(\sqrt{x}-2)$

$=(\sqrt{x}-2)(x+2\sqrt{x}+1)$

$=(\sqrt{x}-2)(\sqrt{x}+1)^2$

\(a,9-3y=\left(3-\sqrt{3y}\right)\left(3+\sqrt{3y}\right)\)

\(b,x^2+2x-4y^2+1=\left(x^2+2x+1\right)-4y^2=\left(x+1\right)^2-\left(2y\right)^2=\left(x-2y+1\right)\left(x+2y+1\right)\)