Problem Solving

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

why isn't this 1/2?

davo45 wrote:if x=-1, then (x^4 - x^3 + x^2) / (x-1)

why isn't this 1/2?

(x^4 - x^3 + x^2) / (x-1) = (-1)^4-(-1)^3+(-1)^2/[(-1-1)] = 1-(-1)+1/(-2) = 3/-2 = -3/2

here, -x^3 = (-1)*x^3
we first need to execute the exponential operation, then multiply by (-1) --> (-1)*(-1)^3=1

Thus, (x^4 - x^3 + x^2) / (x-1) = [(-1)^4 + (-1)*(-1)^3 + (-1)^2)]/(-1-1) = (1+1+1)/(-2) = -3/2

anshumishra wrote:

davo45 wrote:if x=-1, then (x^4 - x^3 + x^2) / (x-1)

why isn't this 1/2?

(x^4 - x^3 + x^2) / (x-1) = (-1)^4-(-1)^3+(-1)^2/[(-1-1)] = 1-(-1)+1/(-2) = 3/-2 = -3/2

Hi there!

To avoid mistakes, it´s (in general) better to simplify the expression BEFORE substituting!

One possible way to do this (focusing on the fact that our denominator is x-1) is:

x^4-x^3+x^2 = x^3*(x-1) +x^2 , therefore this expression over (x-1) is surely equal to x^3 + x^2/(x-1)

Only now I would substitute: (-1)^3 equals -1 and x^2/(x-1) equals 1/(-2) = -1/2, therefore

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

Regards,
Fabio.

P.S.: the way you approach easy problems shows the strength you have to deal with harder ones... therefore (when you have the official answer) THINK about your approach even after you found the right alternative!!