Which of the following expressions is(are) a factor of 3 x 2 + 20 x - 63 ? x -

Question

Which of the following expressions is(are) a factor of 3 x 2 + 20 x - 63 ? x - 9 3 x - 7

Accepted Answer

Choice B is correct. The given expression can be factored by first finding two values whose sum is 20 and whose product is 3 - 63 , or - 189 . Those two values are 27 and - 7 . It follows that the given expression can be rewritten as 3 x 2 + 27 x - 7 x - 63 . Since the first two terms of this expression have a common factor of 3 x and the last two terms of this expression have a common factor of - 7 , this expression can be rewritten as 3 x x + 9 - 7 x + 9 . Since the two terms of this expression have a common factor of x + 9 , it can be rewritten as 3 x - 7 x + 9 . Therefore, expression II, 3 x - 7 , is a factor of 3 x 2 + 20 x - 63 , but expression I, x - 9 , is not a factor of 3 x 2 + 20 x - 63 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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