Let's perform the synthetic division

#color(white)(aaaa)##-3##|##color(white)(aaaa)##1##color(white)(aaaa)##19##color(white)(aaaaaa)##108##color(white)(aaaa)##236##color(white)(aaaaa)##176#

#color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaa)##-3##color(white)(aaaaa)##-48##color(white)(aaa)##-180##color(white)(aaa)##-168#

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

#color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaa)##16##color(white)(aaaaaa)##60##color(white)(aaaaaa)##56##color(white)(aaaaaa)##color(red)(8)#

The remainder is #8# and the quotient is #=x^3+16x^2+60x+56#

Apply the remainder theorem for verification

When a polynomial #f(x)# is divided by #(x-c)#, we get

#f(x)=(x-c)q(x)+r#

Let #x=c#

Then,

#f(c)=0+r#

Here,

#f(x)=x^4+19x^3+108x^2+236x+176#

Therefore,

#f(-3)=(-3)^4+19*(-3)^3+108(-3)^2+236*(-3)+176#

#=8#

The remainder is #=8#