Let's perform the synthetic division
Let f(x)=3x^4-2x^3+5x^2-4x-2
Let's perform the synthetic division
color(white)(aaaa)-1color(white)(aaaaa)|color(white)(aaaa)3color(white)(aaaaaa)-2color(white)(aaaaaa)5color(white)(aaaaa)-4color(white)(aaaaa)-2
color(white)(aaaaaaaaaaaa)_________
color(white)(aaaa)color(white)(aaaaaaa)|color(white)(aaaa)color(white)(aaaaaaa)-3color(white)(aaaaaaa)5color(white)(aaaaa)-10color(white)(aaaa)14
color(white)(aaaaaaaaaaaa)________
color(white)(aaaa)color(white)(aaaaaaa)|color(white)(aaaa)3color(white)(aaaaaa)-5color(white)(aaaaaaa)10color(white)(aaaa)-14color(white)(aaaaa)color(red)(12)
f(x)=(3x^3-5x^2+10x-14)+12/(x+1)
The remainder is =-2