Given equation is

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

Substitution

#f(x) = f(3) = -3^3 + (3 * -3^2) - (2*-3) + 5 = 53#

Synthetic Division

#color(white)(aa)-3color(white)(aa)|color(white)(aa)1color(white)(aaaa)3color(white)(aa)-2color(white)(aa)5#

#color(white)(aaaaaaa)|color(white)(aa)darrcolor(white)(a)-3color(white)(aaaa)0color(white)(aa)6#

#color(white)(aaaaaaa)----------#

#color(white)(aaaaaaaaaaaa)1color(white)(aaa)0color(white)(aa)-2color(white)(aa)11#

Quotient #Q = x^2 - 2#, Remainder #R = 11 / (x + 3)#