{"@context":"https://schema.org/","@type":"Quiz","name":"

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

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-215"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

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

","comment":{"@type":"Comment","text":"

Choice B is correct. The given expression may be rewritten as $\\bm{x}^{2}+8\\bm{x}-5\\bm{x}-40$. Since the first two terms of this expression have a common factor of $\\bm{x}$ and the last two terms of this expression have a common factor of $-5$, this expression may be rewritten as $\\bm{x}(\\bm{x})+\\bm{x}(8)-5(\\bm{x})-5(8)$, or $\\bm{x}(\\bm{x}+8)-5(\\bm{x}+8)$. Since each term of this expression has a common factor of $(\\bm{x}+8)$, it may be rewritten as $(\\bm{x}-5)(\\bm{x}+8)$.

Alternate approach: An expression of the form $\\bm{x}^{2}+b\\bm{x}+c$, 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 $(\\bm{x}-5)(\\bm{x}+8)$.

Choice A is incorrect. This expression is equivalent to $x^{2}+6x-40$, not $x^{2}+3x-40$.

Choice C is incorrect. This expression is equivalent to $x^{2}-3x-40$, not $x^{2}+3x-40$.

Choice D is incorrect. This expression is equivalent to $x^{2}-6x-40$, not $x^{2}+3x-40$.

"},"encodingFormat":"text/markdown","text":"

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

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$(x-4)(x+10)$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$(x-8)(x+5)$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$(x-10)(x+4)$

"}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$(x-5)(x+8)$

","comment":{"@type":"Comment","text":"

Choice A is incorrect. This expression is equivalent to $x^{2}+6x-40$, not $x^{2}+3x-40$.

Choice C is incorrect. This expression is equivalent to $x^{2}-3x-40$, not $x^{2}+3x-40$.

Choice D is incorrect. This expression is equivalent to $x^{2}-6x-40$, not $x^{2}+3x-40$.

"},"answerExplanation":{"@type":"Comment","text":"

Choice A is incorrect. This expression is equivalent to $x^{2}+6x-40$, not $x^{2}+3x-40$.

Choice C is incorrect. This expression is equivalent to $x^{2}-3x-40$, not $x^{2}+3x-40$.

Choice D is incorrect. This expression is equivalent to $x^{2}-6x-40$, not $x^{2}+3x-40$.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-215"}