5x^4+12x^3+17x^2+9x-7
=(5x^4+12x^3+7x^2)+(10x^2+9x-7)
=x^2(x+1)(5x+7)+(2x-1)(5x+7)
=(5x+7)[x^2(x+1)+2x-1]
=(5x+7)(x^3+x^2+2x-1).