factor the given polynomial.

\3t^7 + 18t^6 + 15t^5 =\

if the expression cannot be factored then answer with prime.

Question

factor the given polynomial.

\3t^7 + 18t^6 + 15t^5 =\

if the expression cannot be factored then answer with prime.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Greatest Common Factor", "Polynomial Factoring" ], "new_concepts": [ "Factoring Trinomials" ], "current_concepts": [ "Greatest Common Factor", "Polynomial Factoring", "Factoring Trinomials" ] } ## Factor out the greatest common factor Using the *Greatest Common Factor* knowledge point $$ 3t^7 + 18t^6 + 15t^5 = 3t^5(t^2 + 6t + 5) $$ ## Factor the remaining quadratic trinomial Using the *Polynomial Factoring* knowledge point $$ \begin{aligned} &t^2 + 6t + 5 = (t + 1)(t + 5)\ &3t^7 + 18t^6 + 15t^5 = 3t^5(t + 1)(t + 5) \end{aligned} $$ Factor the given polynomial. $3t^7 + 18t^6 + 15t^5 =$ $3t^5(t + 1)(t + 5)$ { "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

Factor the remaining quadratic trinomial

Answer: