The factor of the provided polynomial completely by taking out the greatest common factor from the polynomial is,
[tex]3a^2y(a^2y^2 - 4ay +2)[/tex]
The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.
The given polynomial in the problem is,
[tex]3a^4y^3 + 12a^3y^2 +6a^2y.[/tex]
Take out the greatest common factor from the above expression. As the greatest common factor of the above polynomial is 3 (3, 12, 6), which can divide each terms. Therefore,
[tex]3(a^4y^3 -4a^3y^2 +2a^2y)[/tex]
Now take out the greatest common factor in terms of variable a and y. The lowest power of a is 2 and y is 1. Therefore, the equation become,
[tex]3a^2y(a^2y^2 - 4ay +2)[/tex]
Hence, the factor completely of the provided polynomial by taking out the greatest common factor from the polynomial is,
[tex]3a^2y(a^2y^2 - 4ay +2)[/tex]
Learn more about factor of polynomial here;
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