Find the value of k,for which (x+2) is a factor of (x+1)^7+(3x+k)^3.

Asked by nitinkumarsingh.singh.75 | 12th Aug, 2015, 12:10: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space p o l y n o m i a l. L e t space f open parentheses x close parentheses equals open parentheses x space plus space 1 close parentheses to the power of 7 plus open parentheses 3 x plus k close parentheses cubed
According to given informatiom (x + 2) is a factor of given polynomial.
Hence, according to remainder theorem,  f open parentheses negative 2 close parentheses equals 0
begin mathsize 14px style Substituting space straight x space equals space minus 2 space in space the space polynomial comma left parenthesis straight x plus 1 right parenthesis to the power of 7 plus left parenthesis 3 straight x plus straight k right parenthesis cubed comma space we space have comma left parenthesis negative 2 space plus 1 right parenthesis to the power of 7 plus left parenthesis 3 open parentheses negative 2 close parentheses plus straight k right parenthesis cubed space equals space 0 therefore open parentheses negative 1 close parentheses to the power of 7 space plus open square brackets space open parentheses negative 6 close parentheses space plus space straight k close square brackets cubed space equals space 0 therefore space minus 1 space plus space open parentheses straight k space minus space 6 close parentheses cubed equals space 0 therefore space open parentheses straight k space minus space 6 close parentheses cubed space equals space 1 therefore straight k space minus space 6 space equals space 1 therefore straight k space equals space 7 end style

Answered by Priti Shah | 12th Aug, 2015, 03:52: PM

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