a) \(3x^2-11x+6\)
\(=3x^2-9x-2x+6\)
\(=3x\left(x-3\right)-2\left(x-3\right)\)
\(=\left(x-3\right)\left(3x-2\right)\)
b) \(8x^2-2x-1\)
\(=8x^2-4x+2x-1\)
\(=8x\left(x-\dfrac{1}{2}\right)+2\left(x-\dfrac{1}{2}\right)\)
\(=\left(x-\dfrac{1}{2}\right)\left(8x+2\right)\)
c) \(6x^2+7xy+2y^2\)
\(=6x^2+3xy+4xy+2y^2\)
\(=3x\left(2x+y\right)+2y\left(2x+y\right)\)
\(=\left(2x+y\right)\left(3x+2y\right)\)
d) \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
e) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z\right)\)
\(=x\left(x+y+z\right)\left(y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left[x\left(x+y+z\right)+yz\right]\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+y\right)+z\left(x+y\right)\right]\)
\(=\left(y+z\right)\left(x+y\right)\left(x+z\right)\)
