7.5 factoring trinomials quiz

factor: $x^2+7x+12$

$(x \quad \hat{\diamond} \quad \hat{\diamond})(x \quad \hat{\diamond} \quad \hat{\diamond})$

Question

7.5 factoring trinomials quiz

factor: $x^2+7x+12$

$(x \quad \hat{\diamond} \quad \hat{\diamond})(x \quad \hat{\diamond} \quad \hat{\diamond})$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials" ], "new_concepts": [ "Factoring Trinomials" ], "current_concepts": [ "Factoring Polynomials", "Factoring Trinomials" ] } ## Identify the trinomial coefficients Using the **Factoring Polynomials** knowledge point $$ \begin{aligned} &x^2 + 7x + 12\ &a = 1,\quad b = 7,\quad c = 12 \end{aligned} $$ ## Find factors of the constant term Using the **Factoring Polynomials** knowledge point $$ \begin{aligned} &\text{Find } p, q \text{ such that } p \cdot q = 12 \text{ and } p + q = 7\ &\text{Factors of 12: } (1, 12), (2, 6), (3, 4)\ &3 + 4 = 7 \end{aligned} $$ ## Write the factored form Using the **Factoring Polynomials** knowledge point $$ (x + 3)(x + 4) $$ Factor: $x^2+7x+12$ $(x + 3)(x + 4)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the trinomial coefficients

Find factors of the constant term

Write the factored form

Answer: