(1)
x3+x2+x-3=x^3-x+x^2+2x-3 = x(x-1)(x+1)+(x-1)(x+3)
= (x-1)(x^2+2x+3)
(2)
x3-6x2+11x-6 = x^3-x^2 -(5x^2-11x+6) = x^2(x-1)-(5x-6)(x-1)
= (x-1)(x^2-5x+6)
=(x-1)(x-2)(x-3)
(3)
x4+x3-7x2-x+6 = x^3(x+1) - (7x-6)(x+1)
= (x+1)(x^3-7x+6)
=(x+1)[(x^3-x^2)+x^2-7x+6]
=(x+1)[x^2(x-1)+(x-6)(x-1)]
=(x+1)(x-1)(x^2+x-6)
=(x+1)(x-1)(x-2)(x+3)