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Equivalent expressions SAT question

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

Which expression is equivalent to $x^{2} + 3 x - 40$ ?

ExplanationShow

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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