Divide p over (x-1) with euclidian division we get the quotient: [tex]3x^3+2x^2-6x-4[/tex] Note that -2/3 is also roots of the above polynomial. Checking: [tex]3(-2/3)^3+2(-2/3)^2-6(-2/3)-4=0[/tex] Dividing again with euclidian algorithm we get the quotient: [tex]3x^3+2x^2-6x-4[/tex] over [tex]3x+2[/tex] is [tex]X^2-2[/tex]. Final factorization: [tex]p(x)=(x-1)(3x+2)(x-\sqrt2)(x+\sqrt2)[/tex]
