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# For any real x, which of the following is equivalent to x^6 + x^5 + x^

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Senior Manager
Joined: 02 Jan 2017
Posts: 315
For any real x, which of the following is equivalent to x^6 + x^5 + x^ [#permalink]

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12 Mar 2017, 05:18
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For any real x, which of the following is equivalent to x^6 + x^5 + x^4?

A. x^4(x^3 + x + 1)

B. x^4(x^2 + 1)

C. x^5(x^2 + x + 1)

D. x^4(x^2 + x + 1)

E. x^3(x^2 + x + 1)
[Reveal] Spoiler: OA
Manager
Joined: 25 Nov 2016
Posts: 57
Location: Switzerland
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Re: For any real x, which of the following is equivalent to x^6 + x^5 + x^ [#permalink]

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12 Mar 2017, 09:59
Answer D pretty straightforward just group the x^4 together
SVP
Joined: 11 Sep 2015
Posts: 2069
Re: For any real x, which of the following is equivalent to x^6 + x^5 + x^ [#permalink]

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12 Mar 2017, 10:23
Expert's post
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vikasp99 wrote:
For any real x, which of the following is equivalent to x^6 + x^5 + x^4?

A. x^4(x^3 + x + 1)

B. x^4(x^2 + 1)

C. x^5(x^2 + x + 1)

D. x^4(x^2 + x + 1)

E. x^3(x^2 + x + 1)

The greatest common factor of x^6, x^5 and x^4 is x^4, so we'll factor that out of the original expression
We get: x^6 + x^5 + x^4 = x^4(x^2 + x^1 + 1)

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Re: For any real x, which of the following is equivalent to x^6 + x^5 + x^ [#permalink]

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12 Mar 2017, 11:10
vikasp99 wrote:
For any real x, which of the following is equivalent to x^6 + x^5 + x^4?

A. x^4(x^3 + x + 1)

B. x^4(x^2 + 1)

C. x^5(x^2 + x + 1)

D. x^4(x^2 + x + 1)

E. x^3(x^2 + x + 1)

$$x^6 + x^5 + x^4$$

= $$x^4 ( x^2 + x + 1 )$$

Thus, answer must be (D) $$x^4(x^2 + x + 1)$$
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Re: For any real x, which of the following is equivalent to x^6 + x^5 + x^ [#permalink]

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15 Mar 2017, 15:51
1
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Expert's post
vikasp99 wrote:
For any real x, which of the following is equivalent to x^6 + x^5 + x^4?

A. x^4(x^3 + x + 1)

B. x^4(x^2 + 1)

C. x^5(x^2 + x + 1)

D. x^4(x^2 + x + 1)

E. x^3(x^2 + x + 1)

We can simplify the given equation by factoring out x^4.

x^4(x^2 + x + 1)

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Re: For any real x, which of the following is equivalent to x^6 + x^5 + x^   [#permalink] 15 Mar 2017, 15:51
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