Answer: Second option :[tex]3x^2y(2x^2y^2+7xy -3)[/tex]Step-by-step explanation:Given expression [tex]6x^4y^3+21x^3y^2-9x^2y[/tex].We need to find greatest common factor (GCF) of all the terms.Let us write all terms in expanded form first.[tex]6x^4y^3 = 2 \times 3 \times x \times x \times x \times x \times y \times y \times y[/tex][tex]21x^3y^2 = 3 \times 7 \times x \times x \times x \times y \times y.[/tex][tex]9x^2y=3 \times 3 \times x \times x \times y.[/tex]We can see that first factor is 3 common, second factor is [tex]x \times x[/tex] and third factor is y.Therefore, GCF would be [tex]3x^2y.[/tex]Now, let us factor out GCF [tex]3x^2y[/tex] and keep the remaining terms inside parenthesis.=[tex]3x^2y(2x^2y^2+7xy -3)[/tex]Therefore, correct option is 2nd option [tex]3x^2y(2x^2y^2+7xy -3)[/tex].