[tex]a)\ \ w(x)=x^3+\sqrt{2}x^2+x=x(x^2+\sqrt{2}x+1)\\\\\\b)\ \ w(x)=(x^2-3x+2)(x^2-2x-3)=(x^2-x-2x+2)(x^2+x-3x-3)=\\\\=(x(x-1)-2(x-1))(x(x+1)-3(x+1))=(x-1)(x-2)(x+1)(x-3)\\\\\\c)\ \ w(x)=(2x^2-5x-3)(2x^2-7x+3)=(2x^2+x-6x-3)(2x^2-x-6x+3)=\\\\=(x(2x+1)-3(2x+1))(x(2x-1)-3(2x-1))=(2x+1)(x-3)(2x-1)(x-3)\\\\=(2x+1)(x-3)^2(2x-1)[/tex]
[tex]d)\ \ w(x)=(x^3+x^2-2x)(x^3+2x^2-15x)=x(x^2+x-2)\cdot x(x^2+2x-15)=\\\\=x\cdot x(x^2+x-2)(x^2+2x-15)=x^2(x^2+2x-x-2)(x^2+5x-3x-15)=\\\\=x^2(x(x+2)-(x+2))(x(x+5)-3(x+5))=x^2(x+2)(x-1)(x+5)(x-3)[/tex]
