If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Sep 25, 2018 3:40 pm

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If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10

OA A

Source: Manhattan Prep

Source: Beat The GMAT — Problem Solving | Tue Sep 25, 2018 3:40 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Sep 25, 2018 10:16 pm

BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10

OA A

Source: Manhattan Prep

Looking at the options, we can deduce that (x – 5) given in the denominator of H gets canceled.

Thus, (x – 5) must be a factor of the numerator of H = x^3 – 6x^2 – x + 30

x^3 – 6x^2 – x + 30
x^2(x – 5) – x^2 – x + 30
x^2(x – 5) – x(x – 5) – 6x + 30
x^2(x – 5) – x(x – 5) – 6(x – 5)

(x – 5)(x^2 – x – 6)

Thus,

H = (x^3 – 6x^2 – x + 30) / (x – 5)

= (x – 5)(x^2 – x – 6) / (x – 5)

= x^2 – x – 6; cancelling (x – 5)

The correct answer: A

Hope this helps!

-Jay
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by GMATGuruNY » Wed Sep 26, 2018 2:28 am

BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10

Let x=0, with the result that H = 30/-5 = -6.
Now plug x=0 in the answers to see which yields a value of -6.
Only A works:
x² - x - 6 = 0² - 0 - 6 = -6.

The correct answer is A.

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by Scott@TargetTestPrep » Thu Sep 27, 2018 4:38 pm

BTGmoderatorDC wrote:If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H is equivalent to which of the following?

A. (x^2) - x - 6
B. (x^3) + 3(x^2) + 3x
C. (x^3) - 25
D. (x^3) - 5(x^2) - 3x
E. (x^2) + x + 10

We see that the numerator of H, x^3 - 6x^2 - x + 30, is not a polynomial that can be easily factored. However, since x^3/x (the first term of numerator divided by the first term of the denominator) is x^2 and 30/(-5) (the constant term of numerator divided by the constant term of the denominator) is -6, we see that if H can be simplified, the answer must be choice A: x^2 - x - 6. Now let’s verify it is the case by multiplying it by (x - 5) to see if the product is x^3 - 6x^2 - x + 30.

(x - 5)(x^2 - x - 6)

x^3 - x^2 - 6x - 5x^2 + 5x + 30

x^3 - 6x^2 - x + 30

We see that (x - 5)(x^2 - x - 6) = x^3 - 6x^2 - x + 30; therefore, (x^3 - 6x^2 - x + 30)/(x - 5) = x^2 - x - 6.

Answer: A

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