\(\text{a) }6x-9-x^2\\ =-\left(x^2+6x+9\right)\\ =-\left(x+3\right)^2\) \(\text{b) }5x^3-10x^2y+5xy^2\\ =5x\left(x^2-2xy+y^2\right)\\ =5x\left(x-y\right)^2\)

\(\text{c) }5x^2-10xy+5y^2-20z^2\\ =5\left(x^2-2xy+y^2-4z^2\right)\\ =5\left[\left(x^2-2xy+y^2\right)-4z^2\right]\\ =5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\\ =5\left(x-y-2z\right)\left(x-y+2z\right)\) \(\text{d) }x^2+5x+6\\ =x^2+3x+2x+6\\ =\left(x^2+3x\right)+\left(2x+6\right)\\ =x\left(x+3\right)+2\left(x+3\right)\\ =\left(x+2\right)\left(x+3\right)\)

\(\text{e) }a^2+9a+8\\ =a^2+a+8a+8\\ =\left(a^2+a\right)+\left(8a+8\right)\\ =a\left(a+1\right)+8\left(a+1\right)\\ =\left(a+8\right)\left(a+1\right)\) \(\text{f) }x^2-x-6\\ =x^2-3x+2x-6\\ =\left(x^2-3x\right)+\left(2x-6\right)\\ =x\left(x-3\right)+2\left(x-3\right)\\ =\left(x+2\right)\left(x-3\right)\)

\(\text{g) }x^2+6x+5\\ =x^2+x+5x+5\\ =\left(x^2+x\right)+\left(5x+5\right)\\ =x\left(x+1\right)+5\left(x+1\right)\\ =\left(x+1\right)\left(x+5\right)\)

\(\text{h) }x^3-3x+2\\=x^3-4x+x+2-2x^2+2x^2+2\\ =\left(x^3-2x^2+x\right)-\left(2x^2-4x+2\right)\\ = x\left(x^2-2x+1\right)-2\left(x^2-2x+1\right)\\ =\left(x-2\right)\left(x^2-2x+1\right)\\ =\left(x-2\right)\left(x-1\right)^2\)