Verified Answer :

taskmasters

"(x^2y + 6)" is the one among the following choices given in the question that is one of the factors of x^2y^3 - 11x^2y + 6y^2 - 66. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer that has actually come to your desired help.

The correct answer is:

A.) (x^2y + 6)  

Explanation:

In order to factor this, we will use factoring by grouping.  To do this, we first break the polynomial into two groups by placing parentheses around the first two terms and around the second two terms:

(x²y³-11x²y)+(6y²-66)

Next, we factor out the GCF of each group.  For the first group, both terms have an x² and a y; there are no numbers in common (other than 1).  Factoring this out,

x²y(y²-11)+(6y²-66)

The GCF of the second group is 6, as both terms are divisible by 6:

x²y(y²-11)+6(y²-11)

We look to the remaining terms in parentheses.  If we have worked correctly, they should be the same.  They are.  This is now the GCF of the polynomial, since it is common to both terms:

(y²-11)(x²y+6)