which expression has an equivalent value to $x^2 + 9x + 8$ for all values of $x$?

$(x + 1)(x + 8)$
$(x + 2)(x + 6)$
$(x + 4)(x + 4)$
$(x + 5)(x + 4)$

Question

which expression has an equivalent value to $x^2 + 9x + 8$ for all values of $x$?

$(x + 1)(x + 8)$
$(x + 2)(x + 6)$
$(x + 4)(x + 4)$
$(x + 5)(x + 4)$

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 the quadratic expression $$ x^2 + 9x + 8 $$ ## Find factors that multiply to 8 and add to 9 $$ \begin{aligned} &\text{Factors of 8: } 1 \times 8 = 8 \ &\text{Sum of factors: } 1 + 8 = 9 \end{aligned} $$ ## Write the factored form $$ (x + 1)(x + 8) $$

(x + 1)(x + 8)

(x + 2)(x + 6)

(x + 4)(x + 4)

(x + 5)(x + 4)

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

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QUESTION IMAGE

Question

Explanation:

Identify the quadratic expression

Find factors that multiply to 8 and add to 9

Write the factored form

Answer: