How do you use synthetic division to divide #X^3 + 2x^2 - 5x - 6 div (x + 3)#?

1 Answer
Jul 5, 2018

Answer:

The remainder is #0# and the quotient is #=x^2-x-2#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-3##|##color(white)(aaaa)##1##color(white)(aaaaa)##2##color(white)(aaaaaa)##-5##color(white)(aaaaa)##-6#

#color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaa)##-3##color(white)(aaaaaaa)##3##color(white)(aaaaaaa)##6#

#color(white)(aaaaaaaaa)###_________________________________________________________##

#color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaa)##-1##color(white)(aaaaaa)##-2##color(white)(aaaaaa)##color(red)(0)#

The remainder is #0# and the quotient is #=x^2-x-2#

Therefore,

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

Also,

If #f(x)=x^3+2x^2-5x-6#

#f(-3)=(-3)^3+2(-3)^2-5(-3)-6#

#=-27+18+15-6#

#=0#