Sir, First of all i couldn't understand the last step. The choices for this question is: 1. x-1 2. x+1 3. x 4. -x

Asked by Gurinder | 18th Dec, 2015, 12:16: AM

Expert Answer:

R e p o n s e space t o space y o u r space p r e v i o u s space q u e r y colon  L e t space f open parentheses x close parentheses equals x to the power of 47 plus 1 g open parentheses x close parentheses equals x squared minus 1 equals open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses T h u s comma space w h e n space w e space d i v i d e space f open parentheses x close parentheses space b y space g open parentheses x close parentheses comma space w e space h a v e comma P open parentheses x close parentheses equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals fraction numerator x to the power of 47 plus 1 over denominator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses end fraction W e space k n o w space t h a t comma space x to the power of n plus 1 space i s space d i v i s i b l e space b y space x plus 1 space i f space n space i s space o d d. A n d space s i n c e space 47 space i s space o d d comma space w e space h a v e comma space x to the power of 47 plus 1 space i s space d i v i s i b l e space b y space x plus 1. T h u s comma space w e space n e e d space t o space f i n d space t h e space r e m a i n d e r space w h e n space f open parentheses x close parentheses space i s space d i v i d e d space b y space x minus 1. T h e r e f o r e comma space t h e space r e m a i n d e r space i s space f open parentheses 1 close parentheses equals 1 to the power of 47 plus 1 equals 2   R e s p o n s e space t o space y o u r space c u r r e n t space q u e r y colon  T h i s space p a r t space t h e space a b o v e space r e s p o n s e space i s space i n c o r r e c t T h u s comma space w e space n e e d space t o space f i n d space t h e space r e m a i n d e r space w h e n space f open parentheses x close parentheses space i s space d i v i d e d space b y space x minus 1. T h e r e f o r e comma space t h e space r e m a i n d e r space i s space f open parentheses 1 close parentheses equals 1 to the power of 47 plus 1 equals 2  P l e a s e space i g n o r e space t h e space a b o v e space p a r t  I n space a space p o l y n o m i a l space d i v i s i o n space w e space n e e d space t o space d i v i d e space t h e space d i v i d e n d space t i l l space t h e space d e g r e e space o f space t h e space d i v i d e n d space i s space l e s s space t h a n space t h e d e g r e e space o f space t h e space d i v i s o r. D e g r e e space o f space t h e space d i v i s o r space i s space 2 T h u s space d i v i s i o n space p r o c e s s space c o n t i n u e s comma space t i l l space t h e space d e g r e e space o f space t h e space n e w space d i v i d e n d space i s space 1. L e t space n e w space d i v i d e n d space equals space A x plus B comma space w h e r e space A space a n d space B space r e space c o n s t a n t s.  W h e n space x to the power of 47 plus 1 space i s space d i v i d e d space b y space x squared minus 1 comma space t h e space q u o t i e n t space w i l l space b e x to the power of 45 plus x to the power of 43 plus x to the power of 41 plus... plus x W h e n space t h e space l a s t space t e r m comma x space i n space t h e space q u o t i e n t space i s space m u l t i p l i e d space w i t h space x squared space i n space t h e space d i v i s o r comma x cubed space t e r m space i s space g e t t i n g space c a n c e n l l e d space w i t h space t h e space p r e v i o u s space t e r m.  W h e n space t h e space l a s t space t e r m comma x space i n space t h e space q u o t i e n t space i s space m u l t i p l i e d space w i t h space minus 1 space i n space t h e space d i v i s o r comma x space t e r m space i s space a p p e a r i n g a s space a space n e w space d i v i d e n d. space T h u s comma space x plus 1 space i s space t h e space n e w space d i v i d e n d. S i n c e space t h e space d e g r e e space o f space t h e space d i v o r space i s space l e s s space t h a n space t h e space d e g r e e space o f space t h e space d i v i s o r comma space w e space w i l l space s t o p space t h e space d i v i s i o n space p r o c e s s H e n c e space x plus 1 space i s space t h e space r e m a i n d e r. space

Answered by Vimala Ramamurthy | 19th Dec, 2015, 02:17: PM

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