[tex]1a)\\\\w(x)=6x^4-15x^3+6x^2=3x^2(2x^2-5x+2)=3x^2(2x^2-4x-x+2)=\\\\=3x^2[2x( x -2x)-(x-2) ]=3x^2(x-2)(2x-1)\\\\2a)\\\\w(x)=9x^5-x^3=x^3(9x^2-1)=x^3(3x -1)(3x+1)\\\\b)\\\\ -8x^4-40x^3-50x^2=-2x^2(4x^2+20x+25)=-2x^2(2x+5)^2[/tex]
[tex]3a)\\\\x^3-5\sqrt{5}=(x-\sqrt{5})(x^2+\sqrt{5}x+5)\\\\a^3-b^3=(a-b)(a^2+ab+b^2)\\\\b)\\\\w(x)=(4x^2-1)^2-9x^2=16x^4-8x^2+1-9x^2=16x^4-17x^2+1[/tex]
[tex]5a)\\\\ x^2(x^3-8)+10x(x^3-8)+25(x^3-8)=(x^3-8)(x^2+10x+25)=\\\\=(x-2)(x^2+2x+4)(x+5)^2 \\\\b)\\\\x^4-25x^3+4x^2-100x=x^3(x-25)+4x(x-25)=(x^3+4x)(x-25)=x(x^2+4)(x-25)[/tex]
