find the sum and classify the polynomial based on degree and number of terms.
\3n^2(5n^2 - 2n + 1) + (4n^2 - 11n^4 - 9)\

$3^{\text{rd}}$ degree polynomial with 3 terms
$4^{\text{th}}$ degree polynomial with 4 terms
$3^{\text{rd}}$ degree polynomial with 4 terms
$4^{\text{th}}$ degree polynomial with 3 terms

Question

find the sum and classify the polynomial based on degree and number of terms.
\3n^2(5n^2 - 2n + 1) + (4n^2 - 11n^4 - 9)\

$3^{\text{rd}}$ degree polynomial with 3 terms
$4^{\text{th}}$ degree polynomial with 4 terms
$3^{\text{rd}}$ degree polynomial with 4 terms
$4^{\text{th}}$ degree polynomial with 3 terms

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Polynomial Addition", "Combining Like Terms", "Polynomial Classification", "Degree of Polynomials" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Polynomial Addition", "Combining Like Terms", "Polynomial Classification", "Degree of Polynomials" ] } ## Expand the first term using the distributive property $$ 3n^2(5n^2 - 2n + 1) = 15n^4 - 6n^3 + 3n^2 $$ ## Add the second polynomial and combine like terms $$ \begin{aligned} &(15n^4 - 6n^3 + 3n^2) + (4n^2 - 11n^4 - 9) \ &= (15n^4 - 11n^4) - 6n^3 + (3n^2 + 4n^2) - 9 \ &= 4n^4 - 6n^3 + 7n^2 - 9 \end{aligned} $$ ## Classify the resulting polynomial $$ \begin{aligned} &\text{Degree: } 4 \quad (\text{highest exponent is } 4) \ &\text{Number of terms: } 4 \quad (4n^4, -6n^3, 7n^2, -9) \end{aligned} $$

(A) 3rd degree polynomial with 3 terms

(B) 4th degree polynomial with 4 terms

(C) 3rd degree polynomial with 4 terms

(D) 4th degree polynomial with 3 terms

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Classification" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the first term using the distributive property

Add the second polynomial and combine like terms

Classify the resulting polynomial

Answer: