solve the following equation by factoring. separate multiple answers with a comma, if necessary.

\(x + 1)(x + 2) = 30\

Question

solve the following equation by factoring. separate multiple answers with a comma, if necessary.

\(x + 1)(x + 2) = 30\

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": [ "FOIL Method", "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "FOIL Method", "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property" ] } ## Expand the left side of the equation Using the *FOIL Method* knowledge point $$ (x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2 $$ ## Write the quadratic equation in standard form Using the *Standard Form of Quadratic Equations* knowledge point $$ \begin{aligned} x^2 + 3x + 2 &= 30 \ x^2 + 3x - 28 &= 0 \end{aligned} $$ ## Factor the quadratic expression Using the *Factoring Quadratic Equations* knowledge point $$ x^2 + 3x - 28 = (x + 7)(x - 4) = 0 $$ ## Solve for x using the zero product property Using the *Zero Product Property* knowledge point $$ \begin{aligned} x + 7 = 0 &\implies x = -7 \ x - 4 = 0 &\implies x = 4 \end{aligned} $$ Solve the following equation by factoring. Separate multiple answers with a comma, if necessary. $$(x + 1)(x + 2) = 30$$ $x =$ $-7, 4$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the left side of the equation

Write the quadratic equation in standard form

Factor the quadratic expression

Solve for x using the zero product property

Answer: