How do you evaluate #\frac{z ^ { 3} + 0z ^ { 2} - z + 42}{z - 7}#?

1 Answer
maganbhai P.
Aug 12, 2018

#(z^3+0z^2-z+42)=(z-7)(z^2+7z+48 )+(378)#

Explanation:

#(z^3+0z^2-z+42)div(z-7)#

Using synthetic division :

We have , #p(z)=(z^3+0z^2-z+42) and "divisor : " z=7#

We take , coefficients of #p(z) to 1,0 ,-1,42#

. #7|# #1color(white)(........)0color(white)(......)-1color(white)(........)42#
#ulcolor(white)(...)|# #ul(0color(white)( ........)7color(white)(........)49color(white)(.......)336#
#color(white)(......)1color(white)(.......)7color(white)(........)48color(white)(.......)color(violet)(ul|378|#
We can see that , quotient polynomial :

#q(z)=z^2+7z+48 and"the Remainder"=378#

Hence ,

#(z^3+0z^2-z+42)=(z-7)(z^2+7z+48 )+(378)#

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