which of the following are factors of (x^4 - 16)? select all that apply.

a. (x^2 + 4)
b. (x^2 - 8)
c. (x^2 - 2)
d. (x + 2)

Question

which of the following are factors of (x^4 - 16)? select all that apply.

a. (x^2 + 4)
b. (x^2 - 8)
c. (x^2 - 2)
d. (x + 2)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics" ], "new_concepts": [ "Difference of Squares", "Factoring Higher Degree Polynomials" ], "current_concepts": [ "Factoring Quadratics", "Difference of Squares", "Factoring Higher Degree Polynomials" ] } ## Apply the difference of squares formula $$ x^4 - 16 = (x^2)^2 - 4^2 = (x^2 - 4)(x^2 + 4) $$ ## Factor the quadratic term further $$ x^2 - 4 = x^2 - 2^2 = (x - 2)(x + 2) $$ ## Combine all factors $$ x^4 - 16 = (x^2 + 4)(x - 2)(x + 2) $$

(A) $x^2 + 4$

(B) $x^2 - 8$

(C) $x^2 - 2$

(D) $x + 2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Higher Degree Polynomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the difference of squares formula

Factor the quadratic term further

Combine all factors

Answer: