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# Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x  [#permalink]

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22 Dec 2016, 01:11
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Difficulty:

55% (hard)

Question Stats:

55% (02:01) correct 45% (02:40) wrong based on 99 sessions

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Which of the following cannot be the factor of $$x^4 + 10x^3 + 35x^2 + 50x + 24$$?

(A) x+1

(B) x+2

(C) x+3

(D) x+4

(E) x+5

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Community Reply Senior Manager Joined: 13 Oct 2016 Posts: 356 GPA: 3.98 Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x [#permalink] ### Show Tags 22 Dec 2016, 01:36 1 1 4 $$ax^4 + bx^3 + cx^2 + dx + e$$ Roots of that polynomial will be factors of +/- $$\frac{e}{a}$$ $$24 = 2^3*3$$ Our root can't have $$5$$ as a factor. Answer E ##### General Discussion Intern Joined: 08 Aug 2016 Posts: 18 Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x [#permalink] ### Show Tags 22 Dec 2016, 07:17 1 My solution : Put x=0 in the equation, we get equation =24. Now check the options (put x=0 in the options too) Ans : (E) =5 , as 5 is not the factor of 24 Sent from my Redmi Note 3 using GMAT Club Forum mobile app _________________ कर्मणयेवाधिकारस्ते मा फलेषु कदाचन| Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8125 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x [#permalink] ### Show Tags 25 Dec 2016, 18:39 1 1 In order to factorize $$x^4 + 10x^3 + 35x2 + 50x + 24$$, you should do as shown below. From $$x^4 + 10x^3 + 35x^2 + 50x + 24=(x+a)(x+b)(x+c)(x+d)$$, if you expand this, you get $$x^4 + 10x^3 + 35x^2 + 50x + 24=x^4+………….+abcd$$, which makes 24=abcd. In other words, a=1, b=2, c=3, d=4 all become factors of 24, but from x+5, 5 cannot be the factor of 24, and so you cannot factorize it. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x  [#permalink]

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12 May 2018, 11:25
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Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x   [#permalink] 12 May 2018, 11:25
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