[tex]a)\\\\w(x)=2x^3+3x^2-3x-2=2x^3-2+3x^2-3x=2(x^3-1)+3x(x-1)=\\\\=2(x-1)(x^2+x+1)+3x(x-1)=(x-1)(2(x^2+x+1)+3x)=\\\\=(x-1)(2x^2+2x+2+3x)=(x-1)(2x^2+5x+2)=(x-1)(2x^2+4x+x+2)=\\\\=(x-1)(2x(x+2)+x+2)=(x-1)(x+2)(2x+1)\\\\\\b)\\\\w(x)=x^3+3x^2-6x-8=x^3-8+3x^2-6x=(x-2)(x^2+2x+4)+3x(x-2)=\\\\=(x-2)(x^2+2x+4+3x)=(x-2)(x^2+5x+4)=(x-2)(x^2+4x+x+4)=\\\\=(x-2)(x(x+4)+x+4)=(x-2)(x+4)(x+1)[/tex]
Wykorzystano wzór skróconego mnożenia
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]x^3-1=x^3-1^3=(x-1)(x^2+x\cdot 1+1^2)=(x-1)(x^2+x+1)\\\\x^3-8=x^3-2^3=(x-2)(x^2+x\cdot2+2^2)=(x-2)(x^2+2x+4)[/tex]
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Verified answer
[tex]a)\\\\w(x)=2x^3+3x^2-3x-2=2x^3-2+3x^2-3x=2(x^3-1)+3x(x-1)=\\\\=2(x-1)(x^2+x+1)+3x(x-1)=(x-1)(2(x^2+x+1)+3x)=\\\\=(x-1)(2x^2+2x+2+3x)=(x-1)(2x^2+5x+2)=(x-1)(2x^2+4x+x+2)=\\\\=(x-1)(2x(x+2)+x+2)=(x-1)(x+2)(2x+1)\\\\\\b)\\\\w(x)=x^3+3x^2-6x-8=x^3-8+3x^2-6x=(x-2)(x^2+2x+4)+3x(x-2)=\\\\=(x-2)(x^2+2x+4+3x)=(x-2)(x^2+5x+4)=(x-2)(x^2+4x+x+4)=\\\\=(x-2)(x(x+4)+x+4)=(x-2)(x+4)(x+1)[/tex]
Wykorzystano wzór skróconego mnożenia
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]x^3-1=x^3-1^3=(x-1)(x^2+x\cdot 1+1^2)=(x-1)(x^2+x+1)\\\\x^3-8=x^3-2^3=(x-2)(x^2+x\cdot2+2^2)=(x-2)(x^2+2x+4)[/tex]