Pessimist Singularitarian
#2
January 4th, 2017,
06:39
You could write:
$ \displaystyle 6x^4+17x^3-24x^2-53x+30=\left(6x^4+12x^3\right)+\left(5x^3+10x^2\right)-\left(34x^2+68x\right)+\left(15x+30\right)=6x^3(x+2)+5x^2(x+2)-34x(x+2)+15(x+2)=(x+2)\left(6x^3+5x^2-34x+15\right)$
$ \displaystyle 6x^3+5x^2-34x+15=\left(6x^3+18x^2\right)-\left(13x^2+39x\right)+\left(5x+15\right)=6x^2(x+3)-13x(x+3)+5(x+3)=(x+3)\left(6x^2-13x+5\right)$
$ \displaystyle 6x^2-13x+5=(2x-1)(3x-5)$
And so we have:
$ \displaystyle 6x^4+17x^3-24x^2-53x+30=(x+2)(x+3)(2x-1)(3x-5)$