1.a^4+a^3+a+1
=a^3(a+1)+(a+1)
=(a^3+1)(a+1)
=(a+1)^2(a^2-a+1)
2.x^4y+2x^3y^2-x^2y-2xy^2
=xy(x^3+2x^2y-x-2y)
=xy[x(x^2-1)+2y(x^2-1)]
=xy(x+2y)(x-1)(x+1)
3.x^3-8y^3-x^2-6xy-4y^2
=(x-2y)(x^2+6xy+4y^2)-(x^2+6xy+4y^2)
=(x-2y)(x^2+6xy+4y^2-1)
4.x^2-11x+24
=(x-3)(x-8)