completely factor the trinomial, if possible.

\x^2 + 11x + 28\

Question

completely factor the trinomial, if possible.

\x^2 + 11x + 28\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Finding Factors with Given Sum and Product" ] } ## Identify the trinomial coefficients Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &x^2 + 11x + 28\ &a = 1,\quad b = 11,\quad c = 28 \end{aligned} $$ ## Find factors with given sum and product Using the *Finding Factors with Given Sum and Product* knowledge point $$ \begin{aligned} &\text{Product: } p \cdot q = c = 28\ &\text{Sum: } p + q = b = 11\ &p = 7,\quad q = 4 \end{aligned} $$ ## Write the factored form Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &x^2 + 11x + 28 = (x + p)(x + q)\ &(x + 7)(x + 4) \end{aligned} $$ $(x + 7)(x + 4)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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Question

Explanation:

Identify the trinomial coefficients

Find factors with given sum and product

Write the factored form

Answer: