find the value of c that makes $4x^2 + 12x + c$ a perfect square trinomial.

a. 3
b. 6
c. 9
d. 12

Question

find the value of c that makes $4x^2 + 12x + c$ a perfect square trinomial.

a. 3
b. 6
c. 9
d. 12

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [ "Perfect Square Trinomials", "Completing the Square" ], "current_concepts": [ "Solving Quadratic Equations", "Perfect Square Trinomials", "Completing the Square" ] } ## Identify the structure of a perfect square trinomial $$ (ax + b)^2 = a^2x^2 + 2abx + b^2 $$ ## Compare coefficients with the given expression $$ \begin{aligned} 4x^2 + 12x + c &= a^2x^2 + 2abx + b^2 \ a^2 &= 4 \implies a = 2 \ 2ab &= 12 \implies 2(2)b = 12 \implies 4b = 12 \implies b = 3 \end{aligned} $$ ## Solve for the constant term c $$ c = b^2 = 3^2 = 9 $$

A. 3

B. 6

C. 9

D. 12

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Perfect Square Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the structure of a perfect square trinomial

Compare coefficients with the given expression

Solve for the constant term c

Answer: