a graphic artist is designing a poster to advertise an upcoming event. the only restrictions regarding the poster size is that it must have a length of $3x$ inches and a width of $5x + 9$ inches. find a simplified expression for the area of the poster.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Geometric Polynomial Modeling", "Multiplying Monomial by Polynomial" ], "new_concepts": [], "current_concepts": [ "Geometric Polynomial Modeling", "Multiplying Monomial by Polynomial", "Polynomial Simplification" ] } ## Identify the given dimensions Using the *Geometric Polynomial Modeling* knowledge point $$ \begin{aligned} &\text{Length } (l) = 3x \text{ inches}\ &\text{Width } (w) = 5x + 9 \text{ inches} \end{aligned} $$ ## Set up the area formula Using the *Geometric Polynomial Modeling* knowledge point $$ \text{Area } (A) = l \times w = 3x(5x + 9) $$ ## Multiply the monomial by the polynomial Using the *Multiplying Monomial by Polynomial* knowledge point $$ A = (3x \cdot 5x) + (3x \cdot 9) = 15x^2 + 27x $$ A graphic artist is designing a poster to advertise an upcoming event. The only restrictions regarding the poster size is that it must have a length of $3x$ inches and a width of $5x + 9$ inches. Find a simplified expression for the area of the poster. $15x^2 + 27x$ square inches { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Geometric Polynomial Modeling" ] }

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Question

Explanation:

Identify the given dimensions

Set up the area formula

Multiply the monomial by the polynomial

Answer: