what value of $g$ makes the equation true?

$(x + 7)(x - 4) = x^2 + gx - 28$

-3
-11
11
3

Question

what value of $g$ makes the equation true?

$(x + 7)(x - 4) = x^2 + gx - 28$

-3
-11
11
3

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Distributive Property", "Linear Equations" ] } ## Expand the left side of the equation $$ (x + 7)(x - 4) = x^2 - 4x + 7x - 28 = x^2 + 3x - 28 $$ ## Equate coefficients to solve for g $$ \begin{aligned} x^2 + 3x - 28 &= x^2 + gx - 28 \ g &= 3 \end{aligned} $$

-3

-11

11

3

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

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QUESTION IMAGE

Question

Explanation:

Expand the left side of the equation

Equate coefficients to solve for g

Answer: