How do you use synthetic division to find x=-1 for #P(x)= x^3+2x^2-5x+6 #?

1 Answer
Jun 6, 2017

Answer:

The remainder is #=12# and the quotient is #=x^2+x-6#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-1##color(white)(aaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##2##color(white)(aaaaaa)##-5##color(white)(aaaaa)##6#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaa)##-1##color(white)(aaaaaa)##-1##color(white)(aaaaa)##6#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaaa)##1##color(white)(aaaaaa)##-6##color(white)(aaaa)##color(red)(12)#

The remainder is #=12# and the quotient is #=x^2+x-6#

#(x^3+2x^2-5x+6)/(x+1)=x^2+x-6+12/(x+1)#