multiply.
$(x^4 + 1)(3x^2 + 9x + 2)$

$x^4 + 3x^2 + 9x + 3$
$3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2$
$3x^7 + 9x^6 + 2x^5$
$3x^8 + 9x^4 + 2x^4 + 3x^2 + 9x + 2$

Question

multiply.
$(x^4 + 1)(3x^2 + 9x + 2)$

$x^4 + 3x^2 + 9x + 3$
$3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2$
$3x^7 + 9x^6 + 2x^5$
$3x^8 + 9x^4 + 2x^4 + 3x^2 + 9x + 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Product of Powers", "Distributive Property", "Multiplying Polynomials" ], "new_concepts": [], "current_concepts": [ "Product of Powers", "Distributive Property", "Multiplying Polynomials" ] } ## Apply the distributive property $$ (x^4 + 1)(3x^2 + 9x + 2) = x^4(3x^2 + 9x + 2) + 1(3x^2 + 9x + 2) $$ ## Distribute each term $$ x^4(3x^2) + x^4(9x) + x^4(2) + 1(3x^2) + 1(9x) + 1(2) $$ ## Simplify the terms $$ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 $$

(A) $x^4 + 3x^2 + 9x + 3$

(B) $3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2$

(C) $3x^7 + 9x^6 + 2x^5$

(D) $3x^8 + 9x^4 + 2x^4 + 3x^2 + 9x + 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Polynomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Distribute each term

Simplify the terms

Answer: