Factor out the greatest common factor from the following polynomial. \( 20 a^{6} b^{6}-30 a^{2} b^{2}+30 a b+40 a^{2} b \) Select the correct choice below and, if necessary, fill in the enswer box to camplete your choice. A. \( 20 a^{6} b^{6}-30 a^{2} b^{2}+30 a b+40 a^{2} b= \) (Type your answer in factored form.) B. The polynomial has no common factor other than 1 . B.

To factor out the greatest common factor from the polynomial \( 20 a^{6} b^{6}-30 a^{2} b^{2}+30 a b+40 a^{2} b \), first we identify the GCF of the coefficients: 20, 30, 30, and 40. The GCF is 10. Now, let's find the lowest power of each variable present in all terms: - For \( a \), the lowest power is \( a \) (present in the second, third, and fourth terms). - For \( b \), the lowest power is \( b \) (present in the second, third, and fourth terms). Thus, the GCF of the polynomial is \( 10 a b \). Now, factoring out \( 10 ab \) from each term results in: \[ 10 a b (2 a^{5} b^{5} - 3 a b + 3 + 4 a) \] So the final factored form is: A. \( 20 a^{6} b^{6}-30 a^{2} b^{2}+30 a b+40 a^{2} b = 10 a b (2 a^{5} b^{5} - 3 a b + 3 + 4 a) \)