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

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

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New post 22 Dec 2016, 01:11
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A
B
C
D
E

Difficulty:

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Question Stats:

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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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Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x  [#permalink]

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New post 22 Dec 2016, 01:36
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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
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Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x  [#permalink]

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New post 22 Dec 2016, 07:17
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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

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Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x  [#permalink]

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New post 25 Dec 2016, 18:39
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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
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Re: Which of the following cannot be the factor of x4 + 10x3 + 35x2 + 50x  [#permalink]

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New post 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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