$a) 6x^4+5x^3-38x^2+5x+6$
$=6x^4-12x^3+17x^3-34x^2-4x^2+8x-3x+6$
$=(6x^4-12x^3)+(17x^3-34x^2)-(4x^2-8x)-(3x-6)$
$=6x^3(x-2)+17x^2(x-2)-4x(x-2)-3(x-2)$
$=(6x^3+17x^2-4x-3)(x-2)$
$=(6x^3+18x^2-x^2-3x-x-3)(x-2)$
$=[6x^2(x+3)-x(x+3)-(x+3)](x-2)$
$=(6x^2-x-1)(x+3)(x-2)$
$=(6x^2-3x+2x-1)(x+3)(x-2)$
$=[3x(2x-1)+(2x-1)](x+3)(x-2)$
$=(3x+1)(2x-1)(x+3)(x-2)$
$b) x^4+7x^3+14x^2+14x+4$
$=x^4+4x^2+10x^2+7x^3+14x+4$
$=(x^4+4x^2+4)+(7x^3+14x)+10x^2$
$=(x^2+2)^2+7x(x^2+2)+10x^2$
$=(x^2+2)^2+2x(x^2+2)+5x(x^2+2)+10x^2$
$=(x^2+2)(x^2+2+2x)+5x(x^2+2+2x)$
$=(x^2+5x+2)(x^2+2x+2)$
$c) 2x^4-5x^3-27x^2+25x+50$
$=2x^4+2x^3-7x^3-7x^2-10x^2-10x^2+35x-10x+50$
$=(2x^4+2x^3-10x^2)-(7x^3+7x^2-35x)-(10x^2+10x-50)$
$=2x^2(x^2+x-5)-7x(x^2+x-5)-10(x^2+x-5)$
$=(2x^2-7x-10)(x^2+x-5)$
