Step 1: Write down the given function
[tex]\begin{gathered} f(x)=6x^3-5x^2-3x+2 \\ f(1)=0 \end{gathered}[/tex]
Step 2: Get the factor of f(1)=0
[tex]\begin{gathered} \text{When f(1)=0} \\ (x-1)\text{ is a factor of the function} \end{gathered}[/tex]
Step 3: Get the other factors by dividing the function by (x-1)
[tex]\frac{f(x)}{x-1}=\frac{6x^2-5x^2-3x+2}{x-1}[/tex][tex]undefined[/tex]
Hence,
[tex]\frac{6x^3-5x^2-3x+2}{x-1}=6x^2+x-2[/tex]
To get the other factors, factorize the answer gotten
[tex]\begin{gathered} 6x^2+x-2 \\ 6x^2+4x-3x-2 \\ 2x(3x+2)-1(3x+2) \\ (2x-1)(3x+2) \end{gathered}[/tex]
Hence, the factors are (x-1)(2x-1)(3x+2)
