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ICSE Class 10 Answered

<div>Find the remainder when,&nbsp;<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=19bf94290971c371875e83c808999c0d.png" alt="x cubed" align="middle" />-3a<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=6ab053eb77594dfda3fccfc8db9f9c73.png" alt="x squared" align="middle" />-<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=f8178eb443730c56b0cf6a6c2539e370.png" alt="a squared" align="middle" />x+3<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=62d2209614f22c44db99ec68932ab007.png" alt="a cubed" align="middle" />&nbsp;is divided by (x-a)</div>
Asked by savi1405 | 30 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 | 01 May, 2016, 12:52: PM
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