type the correct answer in the box.

what is the completely factored form of this polynomial?

$18x^5 - 120x^3 - 42x$

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?

$18x^5 - 120x^3 - 42x$

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": [ "Factoring Polynomials" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials", "Greatest Common Factor" ] } ## Factor out the greatest common factor (GCF) $$ \begin{aligned} &\text{Polynomial: } 18x^5 - 120x^3 - 42x \ &\text{GCF of } 18, 120, \text{ and } 42 \text{ is } 6 \ &\text{GCF of } x^5, x^3, \text{ and } x \text{ is } x \ &\text{GCF } = 6x \ &18x^5 - 120x^3 - 42x = 6x(3x^4 - 20x^2 - 7) \end{aligned} $$ ## Factor the remaining trinomial $$ \begin{aligned} &\text{Let } u = x^2 \ &3u^2 - 20u - 7 = (3u + 1)(u - 7) \ &\text{Substitute } u = x^2 \text{ back:} \ &3x^4 - 20x^2 - 7 = (3x^2 + 1)(x^2 - 7) \end{aligned} $$ ## Write the completely factored form $$ 18x^5 - 120x^3 - 42x = 6x(3x^2 + 1)(x^2 - 7) $$ What is the completely factored form of this polynomial? $18x^5 - 120x^3 - 42x$ Write the greatest common factor (GCF) first, and write all factors in standard form. $6x(3x^2 + 1)(x^2 - 7)$ { "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 trinomial

Write the completely factored form

Answer: