e following quadratic equation:

\7x^2 + 13x + 1 = 3\

: using the standard form $ax^2 + bx + c = 0$ of the given quadratic equation, factor the left hand side of the equation into two linear factors.

Question

e following quadratic equation:

\7x^2 + 13x + 1 = 3\

: using the standard form $ax^2 + bx + c = 0$ of the given quadratic equation, factor the left hand side of the equation into two linear factors.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Standard Form of Quadratic Equations", "Factoring Trinomials", "Trinomial Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Standard Form of Quadratic Equations", "Factoring Trinomials", "Trinomial Factoring by Grouping" ] } ## Convert to standard form Using the *Standard Form of Quadratic Equations* knowledge point $$ \begin{aligned} 7x^2 + 13x + 1 &= 3 \ 7x^2 + 13x + 1 - 3 &= 0 \ 7x^2 + 13x - 2 &= 0 \end{aligned} $$ ## Find factors for grouping Using the *Trinomial Factoring by Grouping* knowledge point $$ \begin{aligned} a \cdot c &= 7 \cdot (-2) = -14 \ b &= 13 \ 14 \cdot (-1) &= -14 \ 14 + (-1) &= 13 \end{aligned} $$ ## Split the middle term Using the *Trinomial Factoring by Grouping* knowledge point $$ 7x^2 + 14x - x - 2 = 0 $$ ## Factor by grouping Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} 7x(x + 2) - 1(x + 2) &= 0 \ (7x - 1)(x + 2) &= 0 \end{aligned} $$ $$(7x - 1)(x + 2) = 0$$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Convert to standard form

Find factors for grouping

Split the middle term

Factor by grouping

Answer: