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

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

I. $x-9$

II. $3x-7$

","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-16"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

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

I. $x-9$

II. $3x-7$

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

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 $3x^{2}+27x-7x-63$. Since the first two terms of this expression have a common factor of $3x$ and the last two terms of this expression have a common factor of $-7$, this expression can be rewritten as $3x(x+9)-7(x+9)$. Since the two terms of this expression have a common factor of $(x+9)$, it can be rewritten as $(3x-7)(x+9)$. Therefore, expression II, $3x-7$, is a factor of $3x^{2}+20x-63$, but expression I, $x-9$, is not a factor of $3x^{2}+20x-63$.

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.

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

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

I. $x-9$

II. $3x-7$

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

I only

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

I and II

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

Neither I nor II

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

II only

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-16"}

Which of the following expressions is(are) a factor of $3x^{2}+20x-63$?I. $x-9$II. $3x-7$

Which of the following expressions is(are) a factor of $3x^{2}+20x-63$?I. $x-9$II. $3x-7$

Which of the following expressions is(are) a factor of $3x^{2}+20x-63$?I. $x-9$II. $3x-7$

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

I. $x-9$

II. $3x-7$

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

I. $x-9$

II. $3x-7$

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

I. $x-9$

II. $3x-7$