fully factorise $n^2 + 9n + 20$

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Factorisation", "Trinomial Factoring" ], "new_concepts": [], "current_concepts": [ "Quadratic Factorisation", "Trinomial Factoring" ] } ## Identify the coefficients of the quadratic expression $$ \begin{aligned} &n^2 + 9n + 20\ &a = 1,\quad b = 9,\quad c = 20 \end{aligned} $$ ## Find two numbers that multiply to 20 and add to 9 $$ \begin{aligned} &p \cdot q = 20\ &p + q = 9\ &p = 4,\quad q = 5 \end{aligned} $$ ## Write the expression in factored form $$ (n + 4)(n + 5) $$ $(n + 4)(n + 5)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Factorisation" ] }

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Question

Explanation:

Identify the coefficients of the quadratic expression

Find two numbers that multiply to 20 and add to 9

Write the expression in factored form

Answer: