Question
Thu April 03, 2014 By: Sanjay Padmanabhan

if x=1 a zero of the polynomial xcube-xsquare-x+1

Expert Reply
Thu April 03, 2014
Consider the equation
P open parentheses x close parentheses equals x cubed minus x squared minus x plus 1 I f space x equals 1 space i s space a space z e r o space o f space t h e space a b o v e space p o l y n o m i a l space i t space s h o u l d space s a t i s f y space t h e space e q u a t i o n. T h u s comma space P open parentheses 1 close parentheses equals 1 cubed minus 1 squared minus 1 plus 1 equals 1 minus 1 minus 1 plus 1 equals 0 S o comma space x equals 1 space i s space a space r o o t space o f space t h e space p o l y n o m i a l. N o w space l e t space u s space f a c t o r i s e space t h e space g i v e n space e q u a t i o n space x cubed minus x squared minus x plus 1 D i v i d e space t h e space e q u a t i o n space x cubed minus x squared minus x plus 1 space b y space x minus 1
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