Questions: Divide. (15 v^6 x^5 - 12 v^6 x^6 - 18 v^3 x^2) / (3 v^5 x^4) Simplify your answer as much as possible.

Transcript text: Divide. \[ \left(15 v^{6} x^{5}-12 v^{6} x^{6}-18 v^{3} x^{2}\right) \div\left(3 v^{5} x^{4}\right) \] Simplify your answer as much as possible.

Solution

Solution Steps

Step 1: Identify the Polynomial and the Monomial

Given a polynomial and a monomial, we first identify each term and its respective coefficient and powers.

Step 2: Divide Each Term of the Polynomial by the Monomial

We divide each term's coefficient by the monomial's coefficient and subtract the monomial's powers from the term's powers.

Term 1: Coefficient becomes 5 and powers become [1, 1].
Term 2: Coefficient becomes -4 and powers become [2, 1].
Term 3: Coefficient becomes -6 and powers become [-2, -2].

Step 3: Simplify the Result

Assuming no like terms, the simplified result is directly obtained from the division.

Final Answer:

5 * x^1 * v^1 -4 * x^2 * v^1 -6 * x^-2 * v^-2

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