→ To factorize it we must find the greatest common factor of the 3 terms
∵ The common factor of 3, 6, and 3 is 3
∵ The common factor of x^3, x^2, and x is x
∴ The greatest common factor of the 3 terms is 3x
→ Divide each term by 3x
[tex]\because\frac{3x^3}{3x}=x^2[/tex][tex]\because\frac{6x^2}{3x}=2x[/tex][tex]\because\frac{3x}{3x}=1[/tex][tex]\therefore3x^3+6x^2+3x=3x(x^2+2x+1)[/tex]→ Now we must factorize the bracket into two factors
[tex]\begin{gathered} \because x^2=x\times x \\ \because1=1\times1 \\ \because(x)(1)+(x)(1)=2x \end{gathered}[/tex][tex]\therefore x^2+2x+1=(x+1)(x+1)[/tex]∴ The complete factorization is
[tex]3x^3+6x^2+3x=3x(x+1)(x+1)=3x(x+1)^2[/tex]