How do you divide #(b^3+2b^2-15b+49)div(b+6)# using synthetic division?

1 Answer
Jul 29, 2018

Answer:

#(b^3+2b^2-15b+49)=(b+6)(b^2-4b+9)+(-5)#

Explanation:

#(b^3+2b^2-15b+49)div(b+6)#

Using synthetic division :

We have , #p(b)=b^3+2b^2-15b+49 and "divisor : " b=-6#

We take ,coefficients of #p(b) to 1,2,-15,49#

#-6 |# #1color(white)(........)2color(white)(.......)-15color(white)(.......)49#
#ulcolor(white)(....)|# #ul(0color(white)( .....)-6color(white)(..........)24color(white)(...)-54#
#color(white)(......)1color(white)(......)-4color(white)(........)color(white)(..)9color(white)(.....)color(violet)(ul|-5|#
We can see that , quotient polynomial :

#q(b)=b^2-4b+9 and"the Remainder"=-5#

Hence ,

#(b^3+2b^2-15b+49)=(b+6)(b^2-4b+9)+(-5)#