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What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ?

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Bunuel
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What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   28 Sep 2020, 06:45
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What is the value of x if \(\frac{x^6 +4x^5 - x - 4}{x + 4} = -244\) ?


A. -9

B. \(-\sqrt[4]{244}\)

C. \(-\sqrt[3]{244}\)

D. -3

E. 3
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D
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lipikatiwari
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   28 Sep 2020, 06:55
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IMO D

Explanation: taking x^5 common,

[x^5(x+4) -1(x+4)]/(x+4) = -244
(x+4)(x^5-1)/(x+4) = -244
Cancelling (x+4) from numerator and denominator

We get, x^5-1= -244
x^5 = -243
So, x = -3

Posted from my mobile device
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   28 Sep 2020, 08:38
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Bunuel wrote:
What is the value of x if \(\frac{x^6 +4x^5 - x - 4}{x + 4} = -244\) ?


A. -9

B. \(-\sqrt[4]{244}\)

C. \(-\sqrt[3]{244}\)

D. -3

E. 3

\(\frac{x^6 +4x^5 - x - 4}{x + 4} = -244\)

Or, \(\frac{x^5 (x + 4 ) -1 ( x + 4)}{x + 4} = -244\)

Or, \(\frac{(x + 4 ) ( x^5 - 1 )}{(x + 4)} = -244\)

Or, \(( x^5 - 1 ) = -244\)

Or, \(x^5 = -243\)

Or, \(x^5 = -3^5\)

Or, \(x = -3\), Answer must be (D)
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   28 Sep 2020, 10:22
What is the value of x if \(\frac{(x^6 +4x^5 - x - 4)}{(x + 4)}\) = -244 ?

\(x^6 +4x^5 - x - 4\)=\( x^5 (x+4) -1(x+4)\)= \((x^5-1)(x+4)\)

\(\frac{(x^6 +4x^5 - x - 4)}{(x + 4)}\) = -244
\(\frac{(x^5-1)(x+4)}{(x + 4)}\) = -244
\((x^5-1)\) = -244
\(x^5\) = -243
\(x^5\) = -\(3^5\)
x=-3

Answer is D
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   28 Sep 2020, 17:33
The main point to learn from this problem is that when we see a any fraction a/b = real number
then definitely b can not be zero.
Furthermore, if a= k*b then we can cross off b from both numerator and denominator-the way we did in this problem.
Here we crossed off (x+4).

That's what I want to share.

Thanks.
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   28 Sep 2020, 19:34
Explanation:

(x^6+4x^5 -x-4)/(x+4) = -244

take x^5 common in numerator and simplify further,

(x^5(x+4)-1(x+4))/(x+4) = -244

(x^5-1)=-244
x^5=-243
x=-3

Hence D is the correct answer.
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink] New post   25 Oct 2020, 10:22
\(\frac{x^6 +4x^5 - x - 4}{x + 4} = -244\)

=\(\frac{ x^5 (x+4) - 1(x+4) }{ (x+4)} = -244\)

= \(\frac{(x^5-1)(x+4) }{ (x+4)} = -244\)

= \(x^5 - 1 = -244\)

= \(x^5 = -243\)

= \(x = -3\)
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Re: What is the value of x if (x^6 +4x^5 - x - 4)/(x + 4) = -244 ? [#permalink]
25 Oct 2020, 10:22
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