a) \(x^2+8x+15=x^2+3x+5x+15=\left(x+3\right)\left(x+5\right)\)
b) \(x^2+3x+2=x^2+2x+x+2=\left(x+1\right)\left(x+2\right)\)
c) \(-x^2+7x-6=-x^2+x+6x-6=\left(-x+6\right)\left(x-1\right)\)
d) \(5x^3y-10x^2y^2+5xy^3=5xy\left(x^2-2xy+y^2\right)=5xy\left(x-y\right)^2\)
e) \(2x^2+7x-15=2x^2-3x+10x-15=\left(2x-3\right)\left(x+5\right)\)