question 5 of 5

select all the correct answers.

the owner of a hotel is installing a patio around three sides of her pool as shown.

which statements are true about the expression representing the area of the patio?

the expression representing the area of the patio is a polynomial.
the expression representing the area of the patio is cubic.
the expression representing the area of the patio has a constant term.
the expression representing the area of the patio has four terms.
the expression representing the area of the patio is a trinomial.

Question

question 5 of 5

select all the correct answers.

the owner of a hotel is installing a patio around three sides of her pool as shown.

which statements are true about the expression representing the area of the patio?

the expression representing the area of the patio is a polynomial.
  the expression representing the area of the patio is cubic.
  the expression representing the area of the patio has a constant term.
  the expression representing the area of the patio has four terms.
  the expression representing the area of the patio is a trinomial.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Operations", "Polynomial Degree", "Polynomial Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Operations", "Polynomial Degree", "Polynomial Terms" ] } ## Calculate the area of the patio $$ \begin{aligned} A_{\text{total}} &= 3p(2p^2 + 4p - 6) = 6p^3 + 12p^2 - 18p \ A_{\text{pool}} &= 5(p^2 - 3p + 2) = 5p^2 - 15p + 10 \ A_{\text{patio}} &= A_{\text{total}} - A_{\text{pool}} \ &= (6p^3 + 12p^2 - 18p) - (5p^2 - 15p + 10) \ &= 6p^3 + 7p^2 - 3p - 10 \end{aligned} $$ ## Analyze the polynomial properties $$ \begin{aligned} &\text{Expression: } 6p^3 + 7p^2 - 3p - 10 \ &\text{Type: Polynomial (True)} \ &\text{Degree: } 3 \implies \text{Cubic (True)} \ &\text{Constant term: } -10 \implies \text{Has a constant term (True)} \ &\text{Number of terms: } 4 \implies \text{Has four terms (True)} \ &\text{Trinomial: False (it has four terms, not three)} \end{aligned} $$

The expression representing the area of the patio is a polynomial.

The expression representing the area of the patio is cubic.

The expression representing the area of the patio has a constant term.

The expression representing the area of the patio has four terms.

The expression representing the area of the patio is a trinomial.

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

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Question

Explanation:

Calculate the area of the patio

Analyze the polynomial properties

Answer: