Final answer:
The question asks for the monomial that is not a partial factor of the given polynomial 12x³ y² – 18x²y + 6xy³. After factoring out the greatest common factor, which is 6xy, and examining the factors, we can identify that x², y², and xy are all partial factors. Without additional options, we cannot identify which one is not a factor.
Step-by-step explanation:
The polynomial given is 12x³ y² – 18x²y + 6xy³. To find which monomial is not a partial factor of this polynomial, we first need to factor out the greatest common factor (GCF). The GCF of the terms in the polynomial is 6xy. Therefore, the polynomial can be factored as:
6xy(2x²y – 3x + y²)
Upon examining the monomials provided,
We can see that all of these are factors of the polynomial either in the GCF or in the secowe can see that all of these are factors of the polynomial either in the GCF or in the second factor (2x²y – 3x + y²). Without a complete list of monomials provided, we can't definitively determine which one is not a partial factor, but the ones listed are indeed factors. If there is another monomial not listed here, and it does not appear as a factor in either the GCF or the bracketed expression, then that monomial would be the one not a partial factor of the polynomial.