=6x^2-12x-3x+6

=6x(x-2)-3(x-2)

=(6x-3)(x-2)

ừ hè quên mất 12 với 3

a) Ta có \(6x^2-15x+9=3.\left(2x^2-5x+3\right)=3.\left(2x^2-2x^2-3x+3\right)\)

\(=3.\left[2x.\left(x-1\right)-3.\left(x-1\right)\right]=3.\left(2x-3\right).\left(x-1\right)\)

b) Ta có \(5x^2+12x+7=5x^2+5x+7x+7=5x.\left(x+1\right)+7.\left(x+1\right)\)

\(=\left(x+1\right)\left(5x+7\right)\)

a) \(6x^2-15x+9\)

\(=3\left(2x^2-5x+3\right)\)

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

b) \(5x^2+12x+7\)

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

\(=5x\left(x+1\right)+7\left(x+1\right)\)

\(=\left(x+1\right)\left(5x+7\right)\)

`= 36x^2-90x+225+15x-6x^2`

`= 30x^2-75x+225`

`= 15(2x^2-5x+9)`.

\(a,5x\left(x-3\right)\\ b,\left(x^2-6x+3^2\right)-y^2\\ =\left(x-3\right)^2-y^2\\ =\left(x-3-y\right)\left(x-3+y\right)\)

(2x+1)(x2+x+1)(3x2+3x+1)

6x^5+15x^4+20x^3+15x^2+6x+1

=3x^4(2x+1)+6x^3(2x+1)+7x^2(2x+1)+4x(2x+1)+(2x+1)

=(2x+1)(3x^4+6x^3+7x^2+4x+1)

=(2x+1)(3x^2(x^2+x+1)+3x(x^2+x+1)+(x^2+x+1)

=(2x+1)(x^2+x+1)(3x^2+3x+1)

6x⁵+15x⁴+20x³+15x²+6x+1

= (6x⁵+3x⁴)+(12x⁴+6x³)+(14x³+7x²)+(8x²+4x)+(2x+1)

= (2x+1)(3x⁴+6x³+7x²+4x+1)

= (2x+1)[(3x⁴+3x³+3x²)+(3x³+3x²+3x)+(x²+x+1)]

= (2x+1)(x²+x+1)(3x²+3x+1)

\(2x^4+x^3-22x^2+15x-36\)

\(=\left(2x^4-6x^3\right)+\left(7x^3-21x^2\right)+\left(-x^2+3x\right)+\left(12x-36\right)\)

\(=\left(x-3\right)\left(2x^3+7x^2-x+12\right)\)

\(=\left(x-3\right)\left(\left(2x^3+8x^2\right)+\left(-x^2-4x\right)+\left(3x+12\right)\right)\)

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

c) \(5x^2+3y+15x+xy=5x\left(x+3\right)+y\left(x+3\right)=\left(x+3\right)\left(5x+y\right)\)

d) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+3-y\right)\left(x+3+y\right)\)

e) \(x^2-y^2+2x+1=\left(x^2+2x+1\right)-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)

f) \(x^2-2xy-9+y^2=\left(x^2-2xy+y^2\right)-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)

c: \(5x^2+15x+3y+xy\)

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

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

d: \(x^2+6x+9-y^2\)

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

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

e: \(x^2+2x+1-y^2\)

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

\(=\left(x+1-y\right)\left(x+1+y\right)\)

f: \(x^2-2xy+y^2-9\)

\(=\left(x-y\right)^2-9\)

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

a: \(x^2+12x+36=0\) 

=>\(x^2+2\cdot x\cdot6+6^2=0\)

=>\(\left(x+6\right)^2=0\)

=>x+6=0

=>x=-6

b: \(4x^2-4x+1=0\)

=>\(\left(2x\right)^2-2\cdot2x\cdot1+1^2=0\)

=>\(\left(2x-1\right)^2=0\)

=>2x-1=0

=>2x=1

=>x=1/2

c: \(x^3+6x^2+12x+8=0\)

=>\(x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3=0\)

=>\(\left(x+2\right)^3=0\)

=>x+2=0

=>x=-2