which expression is the factorization of $x^2 + 10x + 21$?

$(x + 3)(x + 7)$
$(x + 4)(x + 6)$
$(x + 6)(x + 15)$
$(x + 7)(x + 14)$

Question

which expression is the factorization of $x^2 + 10x + 21$?

$(x + 3)(x + 7)$
$(x + 4)(x + 6)$
$(x + 6)(x + 15)$
$(x + 7)(x + 14)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Factoring Trinomials", "Polynomial Multiplication" ] } ## Identify coefficients of the quadratic trinomial $$ x^2 + 10x + 21 \implies a = 1, \quad b = 10, \quad c = 21 $$ ## Find two numbers that multiply to 21 and add to 10 $$ \begin{aligned} &p \cdot q = 21 \ &p + q = 10 \ &\implies p = 3, \quad q = 7 \end{aligned} $$ ## Write the factored form $$ x^2 + 10x + 21 = (x + 3)(x + 7) $$

(A) $(x + 3)(x + 7)$

(B) $(x + 4)(x + 6)$

(C) $(x + 6)(x + 15)$

(D) $(x + 7)(x + 14)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic trinomial

Find two numbers that multiply to 21 and add to 10

Write the factored form

Answer: