Factorise:
(i)   x3 - 2x2 - x + 2                         (ii)  x3 - 3x2 - 9x - 5
(iii) x3 + 13x+ 32x + 20                (iv) 2y3 + y2 - 2y - 1

Asked by Turjo Bhattacharjee | 14th Jun, 2015, 09:23: PM

Expert Answer:

l e t space P left parenthesis x right parenthesis space equals space x cubed minus 2 x squared minus x plus 2  F a c t o r s space o f space 2 space a r e space 1 space a n d space 2.  P left parenthesis 1 right parenthesis space equals space 1 minus 2 minus 1 plus 2 equals 0 a l s o P left parenthesis 2 right parenthesis space equals space 8 minus 8 minus 2 plus 2 equals 0  S o space P left parenthesis x right parenthesis equals 0 space a t space x equals 1 space a n d space 2  T h e r e f o r e space b y space F a c t o r space t h e o r e m space left parenthesis x minus 1 right parenthesis space space a n d space left parenthesis x minus 2 right parenthesis space a r e space f a c t o r s space o f space P left parenthesis x right parenthesis space equals x cubed minus 2 x squared minus x plus 2   S t a t e m e n t space o f space F a c t o r space T h e o r e m  space I f space p left parenthesis x right parenthesis space i s space a space p o l y n o m i a l space o f space d e g r e e space n space greater or equal than space 1 space a n d space a space i s space a n y space r e a l space n u m b e r comma space t h e n left parenthesis i right parenthesis space x space – space a space i s space a space f a c t o r space o f space p left parenthesis x right parenthesis comma space i f space p left parenthesis a right parenthesis space equals space 0 comma left parenthesis i i right parenthesis space p left parenthesis a right parenthesis space equals space 0 comma space i f space x space – space a space i s space a space f a c t o r space o f space p left parenthesis x right parenthesis.

Answered by Vijaykumar Wani | 15th Jun, 2015, 11:18: AM

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