a) X^3+2X-3
=X^3-X^2+X^2-X+3X-3
=X^2(X-1)+X(X-1)+3(X-1)
=(X-1)(X^2+X+3)
b)x^3 - 7x + 6
= x^3 - x^2 + x^2 - x - 6x + 6
= x^2(x - 1) + x(x - 1) - 6(x - 1)
= (x - 1)(x^2 + x - 6)
= (x - 1)(x^2 + 3x - 2x - 6)
= (x - 1)[x(x + 3) - 2(x + 3)]
= (x - 1)(x + 3)(x - 2)
c) x^3+5x^2+8x+4
=x^3+x^2+4x^2+4x+4x+4
=x^2(x+1)+4x(x+1)+4(x+1)
=(x+1)(x^2+4x+4)
=(x+1)(x+2)^2
d) X^3-X^2-X-2
=X^3-2X^2+X^2-2X+X-2
=X^2(X-2)+X(X-2)+(X-2)
=(X-2)(X^2+X+1)