9514 1404 393
Answer:
9n^4
Explanation:
The divisor and quotient can be interchanged to find the divisor:
![(18n^6+27n^5-36n^4)/(2n^2+3n-4)=\boxed{\text{Blank 1}}](https://img.qammunity.org/2022/formulas/mathematics/high-school/2cdrrw2fqh8o8td1uj5ny5lwmdoayubflv.png)
Such division is carried out by first finding the quotient of the highest-degree terms:
![(18n^6)/(2n^2)=(18)/(2)n^(6-2)=9n^4](https://img.qammunity.org/2022/formulas/mathematics/high-school/gtm4j7bb83bp6a0v1at3ky542cbttu0ife.png)
This value is used to multiply the denominator and subtract that product from the numerator to find the new numerator. The new numerator is zero, so the value that goes in Blank 1 is ...
9n^4
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The attachment shows the long division.