on dividing x3-5x2+18x-14 by a polynomial g (x), the quotient and remainder were -12x-11and x-1 respectively.Find g (x)

Asked by Chelsea Dhawan | 19th Jul, 2014, 11:36: PM

Expert Answer:

L e t space p left parenthesis x right parenthesis space equals space x cubed space minus 5 x squared space plus 18 x space minus 14 space b e space d i v i d e d space b y space p o l y n o m i a l space g left parenthesis x right parenthesis space t h e n space t h e space q u o t i e n t space i s space q left parenthesis x right parenthesis space equals space minus 12 x space minus 11 space i s space o b t a i n e d space a n d space r e m a i n d e r space r left parenthesis x right parenthesis space space equals space x space minus space 1. space N o w space b y space E u c l i d apostrophe s space D i v i s i o n space L e m m a comma p left parenthesis x right parenthesis space equals space g left parenthesis x right parenthesis. q left parenthesis x right parenthesis space plus space r left parenthesis x right parenthesis T h e n comma space g left parenthesis x right parenthesis space equals space fraction numerator p left parenthesis x right parenthesis space minus space r left parenthesis x right parenthesis over denominator q left parenthesis x right parenthesis end fraction space g left parenthesis x right parenthesis space equals space fraction numerator space x cubed space minus space 5 x squared space plus 18 x space minus 14 space minus space x space plus space 1 over denominator minus 12 x space minus space 11 end fraction g left parenthesis x right parenthesis space equals space fraction numerator space x cubed space minus space 5 x squared space plus 17 x space minus 13 over denominator minus 12 x space minus space 11 end fraction

Solving by long division method,

The above division does not satisfy the Euclids's lemma so the question posted by you is wrong.

Please repost the correct question, so that we can help you better.

Answered by Mili Hariyani | 21st Jul, 2014, 01:17: PM