The factor of the provided polynomial completely by taking out the greatest common factor from the polynomial is,[tex](x+ 5)(7x^2+3)[/tex]What is a factor of polynomial?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]21x^3+ 35x^2 +9x +15[/tex]Take out the common number from the above expression. As the greatest common factor of the above polynomial is 7 x² (21 x³, 35x²) and 3 (9, 15) which can divide the terms. Therefore,[tex]7x^2(x+ 5) +3(x +5)[/tex]Now take out the common group (x+5). Therefore, the equation become,[tex](x+ 5)(7x^2+3)[/tex]Thus, the factor completely of the provided polynomial by taking out the greatest common factor from the polynomial is,[tex](x+ 5)(7x^2+3)[/tex]Learn more about factor of polynomial here;