If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

Question

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

Bunuel · Answer

\frac{x^4 - x^3 + x^2)}{x - 1} =\frac{(-1)^4 - (-1)^3 + (-1)^2)}{-1 - 1} =\frac{1+1+1}{-2}=-\frac{3}{2} .

Answer: A.

mbaiseasy · Answer

=\frac{(-1)^{4}-(-1)^{3}+(-1)^{2}}{(-1-1)}=\frac{1+1+1}{-2}=-\frac{3}{2}

Answer: A

CLIMBTHELADDER · Answer

I found this a frustrating little exercise - even with a low difficulty, it can be easy to make a mistake if you don’t preserve the negative sign. Let’s take a look at the exercise.

x^4 - X^3 + x^2 / x - 1 
1 - 1 + 1 = 1-1+1 = 1.

One could have easily said the value of the numerator is 1. That is, if we didn’t already take the existing negative sign into account. To prevent mistakes like this from happening on the test, remind yourself to work with brackets. Let’s try it out.

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

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

1 + 1 + 1 / -2 = -3/2
 
Answer choice A.

Kinshook · Answer

If x = -1, then (x^4 - x^3 + x^2)/(x - 1) = (1+1+1)/(-2) = -3/2

IMO A

BrentGMATPrepNow · Answer

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

¹ ² ³ ⁵

Now let's work with the given expression (x⁴ - x³ + x²)/(x - 1)
x =  -1 , then (x⁴ - x³ + x²)/(x - 1) =  (-1) ⁴ -  (-1) ³ +  (-1) ²]/ (-1)  - 1]
=  /(-2)
= 3/(-2)
= -3/2

Answer: A

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=6vsQh_C1UH0 Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

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If x = -1, then (x^4 - x^3 + x^2)/(x - 1) =

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