select the correct answer.

what are the x-intercepts of $f(x) = x^3 + 4x^2 - 9x - 36$?

$\bigcirc (1,0), (2,0), (3,0)$
$\bigcirc (-4,0), (-3,0), (3,0)$
$\bigcirc (-6,0), (2,0), (3,0)$
$\bigcirc (-1,0), (2,0), (18,0)$

Question

select the correct answer.

what are the x-intercepts of $f(x) = x^3 + 4x^2 - 9x - 36$?

$\bigcirc (1,0), (2,0), (3,0)$
$\bigcirc (-4,0), (-3,0), (3,0)$
$\bigcirc (-6,0), (2,0), (3,0)$
$\bigcirc (-1,0), (2,0), (18,0)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Factoring", "Zeros of Polynomial Functions" ], "new_concepts": [], "current_concepts": [ "Polynomial Factoring", "Zeros of Polynomial Functions", "Cubic Functions" ] } ## Factor the polynomial by grouping $$ \begin{aligned} f(x) &= x^3 + 4x^2 - 9x - 36 \ &= x^2(x + 4) - 9(x + 4) \ &= (x^2 - 9)(x + 4) \end{aligned} $$ ## Find the zeros of the factored polynomial $$ \begin{aligned} (x - 3)(x + 3)(x + 4) &= 0 \ x &= 3, -3, -4 \end{aligned} $$ ## Determine the coordinates of the x-intercepts $$ (-4, 0), (-3, 0), (3, 0) $$

(A) $(1,0), (2,0), (3,0)$

(B) $(-4,0), (-3,0), (3,0)$

(C) $(-6,0), (2,0), (3,0)$

(D) $(-1,0), (2,0), (18,0)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Zeros of Polynomial Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the polynomial by grouping

Find the zeros of the factored polynomial

Determine the coordinates of the x-intercepts

Answer: