OG2016 PS If x = -1,

[lionsshare]

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.

[Brent@GMATPrepNow]

If x = -1, then (x� - x³ + x²)/(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 (x� - x³ + x²)/(x - 1)
x = -1, then (x� - x³ + x²)/(x - 1) = [(-1)� - (-1)³ + (-1)²]/[(-1) - 1]
= [1 - (-1) + 1]/(-2)
= 3/(-2)
= -3/2

Answer: A

Cheers,
Brent

[jbryant62]

@brent

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

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Hi AbeNeedsAnswers,

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

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

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)� - (-1)³ + (-1)²)/(-1 -1)

From there it's pretty easy:

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

or

-3/2

[Jeff@TargetTestPrep]

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

Answer: A

[Admin1]

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.

Answer: A

[Admin1]

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.

[Brent@GMATPrepNow]

@brent

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

Good catch!
I've edited my response accordingly.

Cheers,
Brent

[ca7ch22]

This equation is solved by substituting -1 in for x. Also remember: a negative to an even power is positive; a negative to an odd power is negative.

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

The answer is A.