what is the completely factored form of $8x^2 - 50$?

$2(x + 5)(x - 5)$
$2(2x - 5)(2x - 5)$
$2(2x + 5)(2x + 5)$
$2(2x + 5)(2x - 5)$

Question

what is the completely factored form of $8x^2 - 50$?

$2(x + 5)(x - 5)$
$2(2x - 5)(2x - 5)$
$2(2x + 5)(2x + 5)$
$2(2x + 5)(2x - 5)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Difference of Squares", "Greatest Common Factor" ], "current_concepts": [ "Greatest Common Factor", "Difference of Squares", "Polynomial Factoring" ] } ## Factor out the greatest common factor $$ 8x^2 - 50 = 2(4x^2 - 25) $$ ## Factor the difference of squares $$ 4x^2 - 25 = (2x)^2 - (5)^2 = (2x + 5)(2x - 5) $$ ## Combine the factors $$ 8x^2 - 50 = 2(2x + 5)(2x - 5) $$

$2(x + 5)(x - 5)$

$2(2x - 5)(2x - 5)$

$2(2x + 5)(2x + 5)$

$2(2x + 5)(2x - 5)$

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

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QUESTION IMAGE

Question

Explanation:

Factor out the greatest common factor

Factor the difference of squares

Combine the factors

Answer: