factor completely.

\9v^7 - 42v^6 + 24v^5\

Question

factor completely.

\9v^7 - 42v^6 + 24v^5\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Algebraic Expressions" ], "new_concepts": [ "Trinomial Factoring" ], "current_concepts": [ "Greatest Common Factor", "Algebraic Expressions", "Trinomial Factoring" ] } ## Factor out the greatest common factor $$ \begin{aligned} &\text{GCF of } (9, 42, 24) = 3\ &\text{GCF of } (v^7, v^6, v^5) = v^5\ &9v^7 - 42v^6 + 24v^5 = 3v^5(3v^2 - 14v + 8) \end{aligned} $$ ## Factor the remaining quadratic trinomial $$ \begin{aligned} &3v^2 - 14v + 8 = 3v^2 - 12v - 2v + 8\ &= 3v(v - 4) - 2(v - 4)\ &= (3v - 2)(v - 4) \end{aligned} $$ ## Combine the factored components $$ 9v^7 - 42v^6 + 24v^5 = 3v^5(3v - 2)(v - 4) $$ Factor completely. $9v^7 - 42v^6 + 24v^5 =$ $3v^5(3v - 2)(v - 4)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Trinomial Factoring" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the remaining quadratic trinomial

Combine the factored components

Answer: