Answer :
Given:
[tex]3x+6x^3+9x^2[/tex]Required:
We need to factorize the given polynomial.
Explanation:
[tex]3x+6x^3+9x^2=6x^3+9x^2+3x[/tex]Take the common multiple 3x.
[tex]3x+6x^3+9x^2=3x(2x^2+3x+1)[/tex][tex]Use\text{ }3x=2x+x.[/tex][tex]3x+6x^3+9x^2=3x(2x^2+2x+x+1)[/tex][tex]3x+6x^3+9x^2=3x(2x(x+1)+1(x+1))[/tex][tex]3x+6x^3+9x^2=3x(2x+1)(x+1)[/tex][tex]3x+6x^3+9x^2=3x(x+1)\left(2x+1\right)[/tex][tex]3x+6x^3+9x^2=(3x^2+3x)\left(2x+1\right)[/tex]Final answer:
[tex]3x+6x^3+9x^2=(3x^2+3x)\left(2x+1\right)[/tex]