How do you divide #(x^3+15x^2+45x-25)div(x+5)# using synthetic division?

2 Answers
Aug 12, 2018

Answer:

#(x^3+15x^2+45x-25)/(x+5)=x^2+10x-5#

Explanation:

#(x^3+15x^2+45x-25)/(x+5)#

#=(x^2(x+5)+10x^2+45x-25)/(x+5)#

#=(x^2(x+5)+10x(x+5)-5x-25)/(x+5)#

#=(x^2cancel((x+5))+10xcancel((x+5))-5cancel((x+5)))/cancel((x+5))#

#=x^2+10x-5#

\0/ Here's our answer !

Aug 12, 2018

Answer:

#(x^3+15x^2+45x-25)=(x+5)(x^2+10x-5 )+(0)#

Explanation:

#(x^3+15x^2+45x-25)div(x+5)#

Using synthetic division :

We have , #p(x)=(x^3+15x^2+45x-25) and "divisor : " x=-5#

We take ,coefficients of #p(x) to 1,15,45,-25#

#-5|# #1color(white)(.......)15color(white)(........)45color(white)(.....)-25#
#ulcolor(white)(....)|# #ul(0color(white)( ....)-5color(white)(....)-50color(white)(..........)25#
#color(white)(......)1color(white)(........)10color(white)(....)-5color(white)(..........)color(violet)(ul|0|#
We can see that , quotient polynomial :

#q(x)=x^2+10x-5 and"the Remainder"=0#

Hence ,

#(x^3+15x^2+45x-25)=(x+5)(x^2+10x-5 )+(0)#