## OG2016 PS If x = -1,

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### OG2016 PS If x = -1,

by lionsshare » Mon Aug 28, 2017 1:28 pm
If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

OA: A

Anyone can please explain how to solve the problem. Thanks.

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### OG2016 PS If x = -1,

by Brent@GMATPrepNow » Mon Aug 28, 2017 1:38 pm
lionsshare wrote:If x = -1, then (xâ�´ - xÂ³ + xÂ²)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2
Algebraic expressions (like the one above) can have many values, depending on the value of the variables that make up the expression.

Take for example the expression 2x + 1
If x = 3, then 2x + 1 = 2(3) + 1 = 6 + 1 = 7
If x = 6.5, then 2x + 1 = 2(6.5) + 1 = 13 + 1 = 14
If x = -5, then 2x + 1 = 2(-5) + 1 = -10 + 1 = -9
etc

Now let's work with the given expression (xâ�´ - xÂ³ + xÂ²)/(x - 1)
x = -1, then (xâ�´ - xÂ³ + xÂ²)/(x - 1) = [(-1)â�´ - (-1)Â³ + (-1)Â²]/[(-1) - 1]
= [1 - (-1) + 1]/(-2)
= 3/(-2)
= -3/2

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Wed Nov 08, 2017 6:41 am, edited 1 time in total.
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by jbryant62 » Tue Aug 29, 2017 1:00 pm
@brent

you said (1-(-1)+1)=1. shouldn't that be 3?

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by [email protected] » Tue Aug 29, 2017 1:59 pm

A couple of times on Test Day, the GMAT is going to 'test' your ability to subtract negatives. That type of math isn't too difficult, but it's likely that one of the wrong answers will be based on a little mistake that you MIGHT make, so you have to be real detail-oriented with your work.

Here, we're essentially asked to "plug in" -1 into four spots in the given equation and solve it.

(-1)^4 = +1
(-1)^3 = -1
(-2)^2 = +1
(-1 - 1) = -2

Thus, we have....
[(1) - (-1) + (1)]/-2 =
[3]/-2 =
-3/2

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by Matt@VeritasPrep » Wed Aug 30, 2017 5:55 pm
lionsshare wrote:If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

OA: A

Anyone can please explain how to solve the problem. Thanks.
Replace every x in the equation with -1:

((-1)â�´ - (-1)Â³ + (-1)Â²)/(-1 -1)

From there it's pretty easy:

(1 - (-1) + 1)/(-2)

or

-3/2

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by Jeff@TargetTestPrep » Mon Sep 04, 2017 10:14 am
lionsshare wrote:If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

(A) -3/2
(B) -1/2
(C) 0
(D) 1/2
(E) 3/2

OA: A
Let's substitute x = -1 for x in our expression:

(x^4 - x^3 + x^2)/(x - 1)

(1 - (-1) + 1)/(-1 - 1)

(1 + 1 + 1)/(-2) = -3/2

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by Admin1 » Tue Sep 05, 2017 6:46 am
Solution:
Recall, that,
(-1)^p = -1 if p is odd
= +1 if p is even.
So, substituting the given value of x into the expression, we have
((+1) - (-1) + (+1)) / ((-1) - 1) = 3/(-2) = - 3/2.

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### OG2016 PS If x = -1,

by Admin1 » Tue Sep 05, 2017 12:39 pm
If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =?

((-1)^4 - (-1)^3 + (-1)^2)/((-1) - 1)
We know that any negative number raised to an odd power results into a negative number and any negative number raised to an even power results in to a positive number.
In other words,
x^n is a negative number if n is odd and
x^n is a positive number number if n is an even number.
Therefore,
((-1)^4 - (-1)^3 + (-1)^2)/((-1) - 1) = (1-(-1)+1)/(-1-1)
= (1 + 1 + 1)/(-2)
= 3/(-2)
= -3/2

Therefore, Option A is the correct answer.

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by Brent@GMATPrepNow » Wed Nov 08, 2017 6:41 am
jbryant62 wrote:@brent

you said (1-(-1)+1)=1. shouldn't that be 3?
Good catch!
I've edited my response accordingly.

Cheers,
Brent
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$$\frac{x^4-x^3+x^2}{\left(x-1\right)}=\frac{\left(-1\right)^4-\left(-1\right)^3+\left(-1\right)^2}{\left(-1\right)-1}=\frac{1-\left(-1\right)+1}{-2}=-\frac{3}{2}$$