How do you use synthetic division to divide #( x^4 + 3x^3 - 5x^2 + 9 ) / ( x + 3 )#?

1 Answer
Jul 4, 2018

Answer:

The remainder is #=-37# and the quotient is #x^3-5x+15#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-3##|##color(white)(aaaa)##1##color(white)(aaaa)##3##color(white)(aaaaaa)##-5##color(white)(aaaaa)##0##color(white)(aaaaaa)##9#

#color(white)(aaaaaaa)####|##color(white)(aaaa)####color(white)(aaa)##-3##color(white)(aaaaaaa)##0##color(white)(aaaaa)##15##color(white)(aaaa)##-45#

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

#color(white)(aaaaaaa)####|##color(white)(aaaa)##1##color(white)(aaaa)##0##color(white)(aaaaaa)##-5##color(white)(aaaa)##15##color(white)(aaaa)##color(red)(-36)#

The remainder is #=-37# and the quotient is #x^3-5x+15#

#(x^4+3x^3-5x^2+0x+9)/(x+3)=(x^3-5x+15)-36/(x+3)#