Is x+1 a factor of x^65+2x^58-3x^35+x^6-4? Explain your answer or show work.

Question

asked Jan 16, 2018 42.3k views

1 Answer

UModeL · Answer 1 · 2018-01-20T06:14:52+0000

By the polynomial remainder theorem,
x+1

is a factor of
x^(65)+2x^(58)-3x^(35)+x^6-4

if the value of the latter polynomial is zero when
x=-1

.

You have

$(-1)^(65)+2(-1)^(58)-3(-1)^(35)+(-1)^6-4=-1+2+3+1-4=1\\eq0$

so
x+1

is not a factor.