Potential Zeros of f(x)

[nycmathguy]

 

[MathLover1]

\(f(x)=2x^3+11x^2-7x-6\)

\(2x^3+11x^2-7x-6=0\)...........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:

\(x=1\)
\(x=-6\)
\(x=-1/2\)

 

[nycmathguy]

\(f(x)=2x^3+11x^2-7x-6\)

\(2x^3+11x^2-7x-6=0\)...........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.