type the correct answer in the box.

what is the completely factored form of this polynomial?

$18x^3 - 120x^2 - 42x$

write the greatest common factor (gcf) first, and write all factors in standard form.

Question

type the correct answer in the box.

what is the completely factored form of this polynomial?

$18x^3 - 120x^2 - 42x$

write the greatest common factor (gcf) first, and write all factors in standard form.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Factoring" ], "new_concepts": [], "current_concepts": [ "Polynomial Factoring", "Greatest Common Factor" ] } ## Factor out the greatest common factor (GCF) $$ \begin{aligned} &\text{Given polynomial: } 18x^3 - 120x^2 - 42x \ &\text{GCF of coefficients } (18, -120, -42) = 6 \ &\text{GCF of variable terms } (x^3, x^2, x) = x \ &\text{GCF } = 6x \ &18x^3 - 120x^2 - 42x = 6x(3x^2 - 20x - 7) \end{aligned} $$ ## Factor the remaining quadratic trinomial $$ \begin{aligned} &\text{Trinomial: } 3x^2 - 20x - 7 \ &\text{Find two numbers that multiply to } 3 \times (-7) = -21 \text{ and add to } -20: \ &-21 \text{ and } 1 \ &3x^2 - 21x + x - 7 = 3x(x - 7) + 1(x - 7) = (3x + 1)(x - 7) \end{aligned} $$ ## Write the completely factored expression $$ 18x^3 - 120x^2 - 42x = 6x(3x + 1)(x - 7) $$ What is the completely factored form of this polynomial? $18x^3 - 120x^2 - 42x$ Write the greatest common factor (GCF) first, and write all factors in standard form. $6x(3x+1)(x-7)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor (GCF)

Factor the remaining quadratic trinomial

Write the completely factored expression

Answer: