divide.

\(-6z^3x^2 + 10z^4x^5) \div (-3z^4x^5)\

simplify your answer as much as possible.

Question

divide.

\(-6z^3x^2 + 10z^4x^5) \div (-3z^4x^5)\

simplify your answer as much as possible.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Division by Monomial", "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Polynomial Division by Monomial", "Exponent Rules", "Simplifying Rational Expressions" ] } ## Rewrite the division as a sum of fractions $$ \frac{-6z^3x^2 + 10z^4x^5}{-3z^4x^5} = \frac{-6z^3x^2}{-3z^4x^5} + \frac{10z^4x^5}{-3z^4x^5} $$ ## Simplify each term using exponent rules $$ \begin{aligned} \frac{-6z^3x^2}{-3z^4x^5} &= 2z^{3-4}x^{2-5} = 2z^{-1}x^{-3} = \frac{2}{zx^3} \ \frac{10z^4x^5}{-3z^4x^5} &= -\frac{10}{3}z^{4-4}x^{5-5} = -\frac{10}{3} \end{aligned} $$ ## Combine the simplified terms $$ \frac{2}{zx^3} - \frac{10}{3} $$ $\frac{2}{zx^3} - \frac{10}{3}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Division by Monomial" ] }

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QUESTION IMAGE

Question

Explanation:

Rewrite the division as a sum of fractions

Simplify each term using exponent rules

Combine the simplified terms

Answer: