what is the completely factored form of this polynomial?

$x^3 + 3x^2 - 6x - 18$

$(x - 2)(x - 3)(x + 3)$

$(x^2 - 6)(x + 3)$

$(x^2 + 3)(x - 6)$

$(x + 6)(x - 1)(x + 3)$

Question

what is the completely factored form of this polynomial?

$x^3 + 3x^2 - 6x - 18$

$(x - 2)(x - 3)(x + 3)$

$(x^2 - 6)(x + 3)$

$(x^2 + 3)(x - 6)$

$(x + 6)(x - 1)(x + 3)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring by Grouping" ], "new_concepts": [], "current_concepts": [ "Factoring by Grouping", "Factoring Polynomials" ] } ## Group the terms of the polynomial $$ (x^3 + 3x^2) - (6x + 18) $$ ## Factor out the greatest common factor from each group $$ x^2(x + 3) - 6(x + 3) $$ ## Factor out the common binomial factor $$ (x^2 - 6)(x + 3) $$

(A) $(x - 2)(x - 3)(x + 3)$

(B) $(x^2 - 6)(x + 3)$

(C) $(x^2 + 3)(x - 6)$

(D) $(x + 6)(x - 1)(x + 3)$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Group the terms of the polynomial

Factor out the greatest common factor from each group

Factor out the common binomial factor

Answer: