representing area with a polynomial expression

find a simplified expression to represent the area of the triangle. the area formula for a triangle is $\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

the expression that represents the area of this triangle is $\square x^2 + \square x + \square\text{ cm}^2$.

Question

representing area with a polynomial expression

find a simplified expression to represent the area of the triangle. the area formula for a triangle is $\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

the expression that represents the area of this triangle is $\square x^2 + \square x + \square\text{ cm}^2$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Area of Triangle", "Polynomial Multiplication" ], "current_concepts": [ "Area of Triangle", "Polynomial Multiplication", "Polynomial Operations" ] } ## Identify given dimensions and formula $$ \begin{aligned} b &= 4x - 2 \ h &= 2x + 12 \ A &= \frac{1}{2}bh \end{aligned} $$ ## Substitute and expand the expression $$ \begin{aligned} A &= \frac{1}{2}(4x - 2)(2x + 12) \ &= (2x - 1)(2x + 12) \ &= 4x^2 + 24x - 2x - 12 \ &= 4x^2 + 22x - 12 \end{aligned} $$ ## Match with the template $$ \text{Template: } \boxed{\quad}x^2 + \boxed{\quad}x + \boxed{\quad} $$ Comparing coefficients: $$ \begin{aligned} \text{Coefficient of } x^2 &= 4 \ \text{Coefficient of } x &= 22 \ \text{Constant term} &= -12 \end{aligned} $$ The expression that represents the area of this triangle is $4$$x^2 +$ $22$$x +$ $-12$ $\text{cm}^2$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Operations" ] }

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Question

Explanation:

Identify given dimensions and formula

Substitute and expand the expression

Match with the template

Answer: