The Remainder Theorem says that the remainder produced dividing polynomial P(x) by (x - a) will be equal to P(a)....so...
(x + 3) = [ x - (-3) ] .....so.. a = -3 and we are substituting (-3) into x^4 - 9x^3 - 5x^2 - 3x + 4 to find the remainder
(-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4 =
81 + 243 - 45 + 9 + 4 =
292