a: \(3x^2+7x-6=3x^2+9x-2x-6\)
\(=3x\cdot\left(x+3\right)-2\left(x+3\right)\)
\(=\left(x+3\right)\left(3x-2\right)\)
b: \(3x^2+3x-6=3\left(x^2+x-2\right)\)
\(=3\left(x^2+2x-x-2\right)\)
\(=3\left[x\left(x+2\right)-\left(x+2\right)\right]=3\left(x+2\right)\left(x-1\right)\)
c: \(3x^2-3x-6=3\left(x^2-x-2\right)\)
\(=3\left(x^2-2x+x-2\right)\)
\(=3\left[x\left(x-2\right)+\left(x-2\right)\right]=3\left(x-2\right)\left(x+1\right)\)
d: \(6x^2-13x+6\)
\(=6x^2-9x-4x+6\)
\(=3x\left(2x-3\right)-2\left(2x-3\right)=\left(2x-3\right)\left(3x-2\right)\)
e: \(6x^2+13x+6=6x^2+9x+4x+6\)
=3x(2x+3)+2(2x+3)
=(2x+3)(3x+2)
f: \(6x^2+15x+6=3\left(2x^2+5x+2\right)\)
\(=3\left(2x^2+4x+x+2\right)\)
\(=3\left[2x\left(x+2\right)+\left(x+2\right)\right]=3\left(x+2\right)\left(2x+1\right)\)
g: \(6x^2-15x+6=3\left(2x^2-5x+2\right)\)
\(=3\left(2x^2-4x-x+2\right)\)
\(=3\left[2x\left(x-2\right)-\left(x-2\right)\right]=3\left(x-2\right)\left(2x-1\right)\)
h: \(6x^2+20x+6=2\left(3x^2+10x+3\right)\)
\(=2\left(3x^2+9x+x+3\right)\)
\(=2\left[3x\left(x+3\right)+\left(x+3\right)\right]\)
=2(x+3)(3x+1)
i: \(6x^2-20x+6=2\left(3x^2-10x+3\right)\)
\(=2\left(3x^2-9x-x+3\right)\)
\(=2\left[3x\left(x-3\right)-\left(x-3\right)\right]=2\left(x-3\right)\left(3x-1\right)\)
j: \(6x^2+12x+6=6\left(x^2+2x+1\right)=6\left(x+1\right)^2\)
k: \(8x^2-2x-3\)
\(=8x^2-6x+4x-3\)
=2x(4x-3)+(4x-3)
=(4x-3)(2x+1)
l: \(8x^2+2x-3=8x^2+6x-4x-3\)
=2x(4x+3)-(4x+3)
=(4x+3)(2x-1)
m: \(-8x^2+5x+3=-8x^2+8x-3x+3\)
=-8x(x-1)-3(x-1)
=(x-1)(-8x-3)
n: \(8x^2-10x-3=8x^2-12x+2x-3\)
=4x(2x-3)+(2x-3)
=(2x-3)(4x+1)
o: \(8x^2+10x-3=8x^2+12x-2x-3\)
=4x(2x+3)-(2x+3)
=(2x+3)(4x-1)
