a) x^4 + 6x^3 + 7x^2 - 6x + 1
b) x^8 +14x^4 + 1
c) x^3 +6x^2 + 11x + 6
a) $x^4 + 6x^3 + 7x^2 - 6x + 1$
$=x^4+9x^2+1+6x^3-2x^2-6x$
$=(x^2+3x-1)^2$
b) $x^8 +14x^4 + 1$
$=(x^8+4x^4+1+4x^6+2x^4+4x^2)-(4x^6-8x^4+4x^2)$
$=(x^4+2x^2+1)^2-(2x^3-2x)^2$
$=(x^4-2x^3+2x^2+2x+1)(x^4+2x^3+2x^2-2x+1)$
c) $x^3 +6x^2 + 11x + 6$
$=(x^3+3x^2+2x)+(3x^2+9x+6)$
$=x(x^2+3x+2)+3(x^2+3x+2)$
$=(x^2+3x+2)(x+3)$
$=(x+1)(x+2)(x+3)$