Find k so that x^2+2x+k is a factor of 2x^4+x^3-14x^2+5x+6

Asked by Shashikantshinha97 | 24th May, 2019, 10:05: PM

Expert Answer:

begin mathsize 16px style Divide space 2 straight x to the power of 4 space plus space straight x cubed space space minus space 14 straight x squared plus space 5 straight x space plus space 6 space by space straight x squared space plus space 2 straight x space plus space straight k comma space we space get
Remainder space equals space left parenthesis 21 space plus space 7 straight k right parenthesis straight x space plus space left parenthesis 6 space plus space 8 straight k space plus space straight k squared right parenthesis
rightwards double arrow space left parenthesis 21 space plus space 7 straight k right parenthesis straight x space plus space left parenthesis 6 space plus space 8 straight k space plus space 2 straight k squared right parenthesis equals 0
rightwards double arrow 21 space plus space 7 straight k space equals space 0
rightwards double arrow space straight k space equals space minus 3 end style

Answered by Yasmeen Khan | 26th May, 2019, 09:19: AM