what is true about the completely simplified sum of the polynomials $3x^2y^3 - 2xy^5$ and $-3x^2y^3 + 2x^4y$?

- the sum is a trinomial with a degree of 5.
- the sum is a trinomial with a degree of 6.
- the sum is a binomial with a degree of 5.
- the sum is a binomial with a degree of 6.

Question

what is true about the completely simplified sum of the polynomials $3x^2y^3 - 2xy^5$ and $-3x^2y^3 + 2x^4y$?

- the sum is a trinomial with a degree of 5.
- the sum is a trinomial with a degree of 6.
- the sum is a binomial with a degree of 5.
- the sum is a binomial with a degree of 6.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Addition", "Polynomial Degree" ], "new_concepts": [ "Polynomial Classification" ], "current_concepts": [ "Polynomial Addition", "Polynomial Degree", "Polynomial Classification" ] } ## Add the polynomials $$ (3x^2y^3 - 2xy^5) + (-3x^2y^3 + 2x^4y) = (3x^2y^3 - 3x^2y^3) - 2xy^5 + 2x^4y = 2x^4y - 2xy^5 $$ ## Determine degree and classification $$ \begin{aligned} &\text{Term 1: } 2x^4y \implies \text{degree } 4 + 1 = 5\ &\text{Term 2: } -2xy^5 \implies \text{degree } 1 + 5 = 6\ &\text{Polynomial degree: } \max(5, 6) = 6\ &\text{Number of terms: } 2 \implies \text{binomial} \end{aligned} $$

The sum is a trinomial with a degree of 5.

The sum is a trinomial with a degree of 6.

The sum is a binomial with a degree of 5.

The sum is a binomial with a degree of 6.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Classification" ] }

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Question

Explanation:

Add the polynomials

Determine degree and classification

Answer: