[ATTACH=full]2090[/ATTACH]
\(f(x)=2x^3+11x^2-7x-6\) \(2x^3+11x^2-7x-6=0\)...........factor completely \(2x^3-x^2+ 13x^2+6x-2x^2-13x-6=0\) \((2x^3-2x^2)+ (13x^2-13x)+(6x-6)=0\) \(2x^2(x-1)+ 13x(x-1)+6(x-1)=0\) \((x - 1) (2x^2 + 13x + 6) = 0\) \((x - 1) (2x^2+x + 12x + 6) = 0\) \((x - 1) ((2x^2 + 12x) +(x+ 6)) = 0\) \((x - 1) (2x(x + 6) +(x+ 6)) = 0\) \((x - 1) (x + 6) (2x + 1) = 0\) zeros: \(x=1\) \(x=-6\) \(x=-1/2\)
If memory serves me right, I greatly struggled with this topic back in my college days. I think the same confusion lingers.