Find the remainder when, x cubed-3ax squared-a squaredx+3a cubed is divided by (x-a)

Asked by savi1405 | 30th Apr, 2016, 02:16: PM

Expert Answer:

R e m a i n d e r space t h e o r e m space s t a t e s space t h a t space t h e space r e m a i n d e r space o f space t h e space d i v i s i o n space o f space a space p o l y n o m i a l space f open parentheses x close parentheses space b y space a space l i n e a r space p o l y n o m i a l space x minus a space i s space e q u a l space t o space f open parentheses a close parentheses.
G i v e n space t h a t comma
f open parentheses x close parentheses equals x cubed minus 3 a x squared minus a squared x plus 3 a cubed
L i n e a r space p o l y n o m i a l equals x minus a
T h u s comma space t h e space r e m a i n d e r space o f space t h e space d i v i s i o n space o f space x cubed minus 3 a x squared minus a squared x plus 3 a cubed space b y space x minus a equals f open parentheses a close parentheses
rightwards double arrow f open parentheses a close parentheses equals a cubed minus 3 a open parentheses a close parentheses squared minus a squared cross times a plus 3 a cubed
rightwards double arrow f open parentheses a close parentheses equals a cubed minus 3 a cubed minus a cubed plus 3 a cubed
rightwards double arrow f open parentheses a close parentheses equals a cubed minus a cubed
rightwards double arrow f open parentheses a close parentheses equals 0
T h u s space t h e space r e m a i n d e r space w h e n space x cubed minus 3 a x squared minus a squared plus 3 a cubed space i s space d i v i d e d space b y space x minus a space i s space 0.

Answered by Vimala | 1st May, 2016, 12:52: PM