How do you divide #(x^3-8x+3)div(x+3)# using synthetic division?

2 Answers
Aug 12, 2018

Answer:

#(x^3-8x+3)/(x+3)=x^2-3x+1#

Explanation:

#(x^3-8x+3)/(x+3)#

#=(x^2(x+3)-3x^2-8x+3)/(x+3)#

#=(x^2cancel((x+3))-3xcancel((x+3))+1cancel((x+3)))/cancel((x+3))#

#=x^2-3x+1#

\0/ Here's our answer !

Aug 12, 2018

Answer:

#(x^3-8x+3)=(x+3)(x^2-3x+1 )+(0)#

Explanation:

#(x^3-8x+3)div(x+3)#

Using synthetic division :

We have , #p(x)=(x^3+0x^2-8x+3) and "divisor : " x=-3#

We take , coefficients of #p(x) to 1,0 ,-8,3#

#-3|# #1color(white)(........)0color(white)(......)-8color(white)(..........)3#
#ulcolor(white)(....)|# #ul(0color(white)( ....)-3color(white)(..........)9color(white)(......)-3#
#color(white)(......)1color(white)(......)-3color(white)(........)1color(white)(..........)color(violet)(ul|0|#
We can see that , quotient polynomial :

#q(x)=x^2-3x+1 and"the Remainder"=0#

Hence ,

#(x^3-8x+3)=(x+3)(x^2-3x+1 )+(0)#