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Equivalent expressions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

$4 a squared, plus 20 a b, plus 25 b squared$

Which of the following is a factor of the polynomial above?

ExplanationShow

Choice B is correct. The first and last terms of the polynomial are both squares such that $4 a, squared, equals, open parenthesis, 2 a, close parenthesis, squared$ and $25 b squared, equals, open parenthesis, 5 b, close parenthesis, squared$ . The second term is twice the product of the square root of the first and last terms: $20 a, b, equals 2, times 2 a, times 5 b$ . Therefore, the polynomial is the square of a binomial such that $4 a, squared, plus 20 a, b, plus 25 b squared, equals, open parenthesis, 2 a, plus 5 b, close parenthesis, squared$ , and $open parenthesis, 2 a, plus 5 b, close parenthesis$ is a factor.

Choice A is incorrect and may be the result of incorrectly factoring the polynomial. Choice C is incorrect and may be the result of dividing the second and third terms of the polynomial by their greatest common factor. Choice D is incorrect and may be the result of not factoring the coefficients.

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