difference between factor theroem and remainder theorem.

Asked by pahiroy1221 | 25th Jul, 2015, 01:44: PM

Expert Answer:

bottom enclose D i v i s i o n space a l g o r i t h m colon end enclose L e t space f left parenthesis x right parenthesis space b e space a space g i v e n space p o l y n o m i a l. L e t space u s space d i v i d e space f left parenthesis x right parenthesis space b y space x minus a T h e r e f o r e comma space f left parenthesis x right parenthesis equals q open parentheses x close parentheses open parentheses x minus a close parentheses plus r left parenthesis x right parenthesis H e r e comma space q left parenthesis x right parenthesis space i s space t h e space q u o t i e n t space o f space t h e space g i v e n space p o l y n o m i a l space a n d space r left parenthesis x right parenthesis space i s space t h e space r e m a i n d e r space o f space t h e space p o l y n o m i a l.  bottom enclose R e m a i n d e r space T h e o r e m end enclose colon W h e n space a space g i v e n space p o l y n o m i a l space i s space d i v i d e d space b y space x minus a comma space t h e n space t h e space r e m a i n d e r space i s space e q u a l space t o space f left parenthesis a right parenthesis. rightwards double arrow f open parentheses a close parentheses equals r open parentheses x close parentheses  bottom enclose F a c t o r space T h e o r e m colon end enclose W h e n space x minus a space i s space a space f a c t o r space o f space t h e space g i v e n space p o l y n o m i a l space t h e n space f left parenthesis a right parenthesis equals 0 I t space i s space a space s p e c i a l space c a s e space o f space R e m a i n d e r space T h e o r e m.

Answered by Vimala Ramamurthy | 26th Jul, 2015, 12:43: PM