Which expression is equivalent to x 2 + 3 x - 40 ?

Question

Accepted Answer

Choice B is correct. The given expression may be rewritten as x 2 + 8 x - 5 x - 40 . Since the first two terms of this expression have a common factor of x and the last two terms of this expression have a common factor of - 5 , this expression may be rewritten as x x + x 8 - 5 x - 5 8 , or x x + 8 - 5 x + 8 . Since each term of this expression has a common factor of x + 8 , it may be rewritten as x - 5 x + 8 . Alternate approach: An expression of the form x 2 + b x + c , where b and c are constants, can be factored if there are two values that add to give b and multiply to give c . In the given expression, b = 3 and c = - 40 . The values of - 5 and 8 add to give 3 and multiply to give - 40 , so the expression can be factored as x - 5 x + 8 . Choice A is incorrect. This expression is equivalent to x 2 + 6 x - 40 , not x 2 + 3 x - 40 . Choice C is incorrect. This expression is equivalent to x 2 - 3 x - 40 , not x 2 + 3 x - 40 . Choice D is incorrect. This expression is equivalent to x 2 - 6 x - 40 , not x 2 + 3 x - 40 .

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