completely factor the given polynomial, if possible. if the polynomial cannot be factored, write nf for your answer.

\x^3 + 14x^2 + 40x\

Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, write nf for your answer.

\x^3 + 14x^2 + 40x\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ], "new_concepts": [], "current_concepts": [ "Factoring Polynomials by GCF", "Factoring Trinomials" ] } ## Factor out the greatest common factor Using the *Factoring Polynomials by GCF* knowledge point $$ x^3 + 14x^2 + 40x = x(x^2 + 14x + 40) $$ ## Factor the remaining quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} &x^2 + 14x + 40 = (x + 4)(x + 10)\ &x^3 + 14x^2 + 40x = x(x + 4)(x + 10) \end{aligned} $$ $x(x + 4)(x + 10)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the remaining quadratic trinomial

Answer: