[tex]\displaystyle x^3-x^2-10x-8=x^3+x^2-2x^2-2x-8x-8=x^2(x+1)-2x(x+1)-8(x+1)=\\(x+1)(x^2-2x-8)=(x+1)(x^2+2x-4x-8)=(x+1)(x(x+2)-4(x+2))=\\(x+1)(x+2)(x-4)[/tex]
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[tex]\displaystyle x^3-x^2-10x-8=x^3+x^2-2x^2-2x-8x-8=x^2(x+1)-2x(x+1)-8(x+1)=\\(x+1)(x^2-2x-8)=(x+1)(x^2+2x-4x-8)=(x+1)(x(x+2)-4(x+2))=\\(x+1)(x+2)(x-4)[/tex]
Verified answer
x^3-x^2-10x-8 = (x+1)(x+2)(x-4)