6x⁴+5x³-38x²+5x+6
=6x⁴-12x³+17x³-34x²-4x²+8x-3x+6
=(6x⁴-12x³)+(17x³-34x²)-(4x²-8x)-(3x-6)
=6x³(x-2)+17x²(x-2)-4x(x-2)-3(x-2)
=(x-2)(6x³+17x²-4x-3)
=(x-2)(6x³+18x²-x²-3x-x-3)
=(x-2)[(6x³+18x²)-(x²+3x)-(x+3)]
=(x-2)[(6x²(x+3)-x(x+3)-(x+3)]
=(x-2)(x+3)(6x²-x-1)
=(x-2)(x+3)(3x+1)(2x-1)